Wreath products

If H and S⊆S_n are groups, the wreath product of H and S is the semidirect product

H wr S = Hⁿ : S where S acts on Hⁿ via S⊆S_n, permuting the n copies of H.

Groups of order 8

		Label	Label	d	ρ	ID
D₄	C₂wrC₂	C2wrC2	D4	4	2+	8,3

Groups of order 18

		Label	Label	d	ρ	ID
C₃xS₃	C₃wrC₂	C3wrC2	C3xS3	6	2	18,3

Groups of order 24

		Label	Label	d	ρ	ID
C₂xA₄	C₂wrC₃	C2wrC3	C2xA4	6	3+	24,13

Groups of order 32

		Label	Label	d	ρ	ID
C₄wrC₂	C₄wrC₂	C4wrC2	C4wrC2	8	2	32,11
C₂²wrC₂	C₂²wrC₂	C2^2wrC2	C2^2wrC2	8		32,27

Groups of order 48

		Label	Label	d	ρ	ID
C₂xS₄	C₂wrS₃	C2wrS3	C2xS4	6	3+	48,48

Groups of order 50

		Label	Label	d	ρ	ID
C₅xD₅	C₅wrC₂	C5wrC2	C5xD5	10	2	50,3

Groups of order 64

		Label	Label	d	ρ	ID
C₂wrC₄	C₂wrC₄	C2wrC4	C2wrC4	8	4+	64,32
C₂wrC₂²	C₂wrC₂²	C2wrC2^2	C2wrC2^2	8	4+	64,138

Groups of order 72

		Label	Label	d	ρ	ID
C₃xC₃:D₄	C₆wrC₂	C6wrC2	C3xC3:D4	12	2	72,30
S₃wrC₂	S₃wrC₂	S3wrC2	S3wrC2	6	4+	72,40

Groups of order 81

		Label	Label	d	ρ	ID
C₃wrC₃	C₃wrC₃	C3wrC3	C3wrC3	9	3	81,7

Groups of order 98

		Label	Label	d	ρ	ID
C₇xD₇	C₇wrC₂	C7wrC2	C7xD7	14	2	98,3

Groups of order 128

		Label	Label	d	ρ	ID
C₈wrC₂	C₈wrC₂	C8wrC2	C8wrC2	16	2	128,67
(C₂xC₄)wrC₂	(C₂xC₄)wrC₂	(C2xC4)wrC2	(C2xC4)wrC2	16		128,628
D₄wrC₂	D₄wrC₂	D4wrC2	D4wrC2	8	4+	128,928
	C₂wrD₄	C2wrD4
Q₈wrC₂	Q₈wrC₂	Q8wrC2	Q8wrC2	16	4-	128,937
C₂³wrC₂	C₂³wrC₂	C2^3wrC2	C2^3wrC2	16		128,1578

Groups of order 160

		Label	Label	d	ρ	ID
C₂xC₂⁴:C₅	C₂wrC₅	C2wrC5	C2xC2^4:C5	10	5+	160,235

Groups of order 162

		Label	Label	d	ρ	ID
C₉xD₉	C₉wrC₂	C9wrC2	C9xD9	18	2	162,3
C₃wrS₃	C₃wrS₃	C3wrS3	C3wrS3	9	3	162,10
C₃²xC₃:S₃	C₃²wrC₂	C3^2wrC2	C3^2xC3:S3	18		162,52

Groups of order 192

		Label	Label	d	ρ	ID
C₄xC₄²:C₃	C₄wrC₃	C4wrC3	C4xC4^2:C3	12	3	192,188
C₂wrA₄	C₂wrA₄	C2wrA4	C2wrA4	8	4+	192,201
C₂²xC₂²:A₄	C₂²wrC₃	C2^2wrC3	C2^2xC2^2:A4	12		192,1540

Groups of order 200

		Label	Label	d	ρ	ID
C₅xC₅:D₄	C₁₀wrC₂	C10wrC2	C5xC5:D4	20	2	200,31
D₅wrC₂	D₅wrC₂	D5wrC2	D5wrC2	10	4+	200,43

Groups of order 242

		Label	Label	d	ρ	ID
C₁₁xD₁₁	C₁₁wrC₂	C11wrC2	C11xD11	22	2	242,3

Groups of order 288

		Label	Label	d	ρ	ID
C₃xC₄²:₄S₃	C₁₂wrC₂	C12wrC2	C3xC4^2:4S3	24	2	288,239
Dic₃wrC₂	Dic₃wrC₂	Dic3wrC2	Dic3wrC2	24	4-	288,389
C₃xC₂⁴:₄S₃	(C₂xC₆)wrC₂	(C2xC6)wrC2	C3xC2^4:4S3	24		288,724
D₆wrC₂	D₆wrC₂	D6wrC2	D6wrC2	12	4+	288,889
A₄wrC₂	A₄wrC₂	A4wrC2	A4wrC2	8	6+	288,1025

Groups of order 320

		Label	Label	d	ρ	ID
C₂xC₂⁴:D₅	C₂wrD₅	C2wrD5	C2xC2^4:D5	10	5+	320,1636

Groups of order 324

		Label	Label	d	ρ	ID
C₃xC₃³:C₄	C₃wrC₄	C3wrC4	C3xC3^3:C4	12	4	324,162
C₃xC₃²:₄D₆	C₃wrC₂²	C3wrC2^2	C3xC3^2:4D6	12	4	324,167

Groups of order 338

		Label	Label	d	ρ	ID
C₁₃xD₁₃	C₁₃wrC₂	C13wrC2	C13xD13	26	2	338,3

Groups of order 375

		Label	Label	d	ρ	ID
C₅xC₅²:C₃	C₅wrC₃	C5wrC3	C5xC5^2:C3	15	3	375,6

Groups of order 392

		Label	Label	d	ρ	ID
C₇xC₇:D₄	C₁₄wrC₂	C14wrC2	C7xC7:D4	28	2	392,27
D₇wrC₂	D₇wrC₂	D7wrC2	D7wrC2	14	4+	392,37

Groups of order 450

		Label	Label	d	ρ	ID
C₁₅xD₁₅	C₁₅wrC₂	C15wrC2	C15xD15	30	2	450,29

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