Wreath products

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

H ≀ 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	C₂≀C₂	C2wrC2	D4	4	2+	8,3

Groups of order 18

		Label	Label	d	ρ	ID
C₃×S₃	C₃≀C₂	C3wrC2	C3xS3	6	2	18,3

Groups of order 24

		Label	Label	d	ρ	ID
C₂×A₄	C₂≀C₃	C2wrC3	C2xA4	6	3+	24,13

Groups of order 32

		Label	Label	d	ρ	ID
C₄≀C₂	C₄≀C₂	C4wrC2	C4wrC2	8	2	32,11
C₂²≀C₂	C₂²≀C₂	C2^2wrC2	C2^2wrC2	8		32,27

Groups of order 48

		Label	Label	d	ρ	ID
C₂×S₄	C₂≀S₃	C2wrS3	C2xS4	6	3+	48,48

Groups of order 50

		Label	Label	d	ρ	ID
C₅×D₅	C₅≀C₂	C5wrC2	C5xD5	10	2	50,3

Groups of order 64

		Label	Label	d	ρ	ID
C₂≀C₄	C₂≀C₄	C2wrC4	C2wrC4	8	4+	64,32
C₂≀C₂²	C₂≀C₂²	C2wrC2^2	C2wrC2^2	8	4+	64,138

Groups of order 72

		Label	Label	d	ρ	ID
C₃×C₃⋊D₄	C₆≀C₂	C6wrC2	C3xC3:D4	12	2	72,30
S₃≀C₂	S₃≀C₂	S3wrC2	S3wrC2	6	4+	72,40

Groups of order 81

		Label	Label	d	ρ	ID
C₃≀C₃	C₃≀C₃	C3wrC3	C3wrC3	9	3	81,7

Groups of order 98

		Label	Label	d	ρ	ID
C₇×D₇	C₇≀C₂	C7wrC2	C7xD7	14	2	98,3

Groups of order 128

		Label	Label	d	ρ	ID
C₈≀C₂	C₈≀C₂	C8wrC2	C8wrC2	16	2	128,67
(C₂×C₄)≀C₂	(C₂×C₄)≀C₂	(C2xC4)wrC2	(C2xC4)wrC2	16		128,628
D₄≀C₂	D₄≀C₂	D4wrC2	D4wrC2	8	4+	128,928
	C₂≀D₄	C2wrD4
Q₈≀C₂	Q₈≀C₂	Q8wrC2	Q8wrC2	16	4-	128,937
C₂³≀C₂	C₂³≀C₂	C2^3wrC2	C2^3wrC2	16		128,1578

Groups of order 160

		Label	Label	d	ρ	ID
C₂×C₂⁴⋊C₅	C₂≀C₅	C2wrC5	C2xC2^4:C5	10	5+	160,235

Groups of order 162

		Label	Label	d	ρ	ID
C₉×D₉	C₉≀C₂	C9wrC2	C9xD9	18	2	162,3
C₃≀S₃	C₃≀S₃	C3wrS3	C3wrS3	9	3	162,10
C₃²×C₃⋊S₃	C₃²≀C₂	C3^2wrC2	C3^2xC3:S3	18		162,52

Groups of order 192

		Label	Label	d	ρ	ID
C₄×C₄²⋊C₃	C₄≀C₃	C4wrC3	C4xC4^2:C3	12	3	192,188
C₂≀A₄	C₂≀A₄	C2wrA4	C2wrA4	8	4+	192,201
C₂²×C₂²⋊A₄	C₂²≀C₃	C2^2wrC3	C2^2xC2^2:A4	12		192,1540

Groups of order 200

		Label	Label	d	ρ	ID
C₅×C₅⋊D₄	C₁₀≀C₂	C10wrC2	C5xC5:D4	20	2	200,31
D₅≀C₂	D₅≀C₂	D5wrC2	D5wrC2	10	4+	200,43

Groups of order 242

		Label	Label	d	ρ	ID
C₁₁×D₁₁	C₁₁≀C₂	C11wrC2	C11xD11	22	2	242,3

Groups of order 288

		Label	Label	d	ρ	ID
C₃×C₄²⋊₄S₃	C₁₂≀C₂	C12wrC2	C3xC4^2:4S3	24	2	288,239
Dic₃≀C₂	Dic₃≀C₂	Dic3wrC2	Dic3wrC2	24	4-	288,389
C₃×C₂⁴⋊₄S₃	(C₂×C₆)≀C₂	(C2xC6)wrC2	C3xC2^4:4S3	24		288,724
D₆≀C₂	D₆≀C₂	D6wrC2	D6wrC2	12	4+	288,889
A₄≀C₂	A₄≀C₂	A4wrC2	A4wrC2	8	6+	288,1025

Groups of order 320

		Label	Label	d	ρ	ID
C₂×C₂⁴⋊D₅	C₂≀D₅	C2wrD5	C2xC2^4:D5	10	5+	320,1636

Groups of order 324

		Label	Label	d	ρ	ID
C₃×C₃³⋊C₄	C₃≀C₄	C3wrC4	C3xC3^3:C4	12	4	324,162
C₃×C₃²⋊₄D₆	C₃≀C₂²	C3wrC2^2	C3xC3^2:4D6	12	4	324,167

Groups of order 338

		Label	Label	d	ρ	ID
C₁₃×D₁₃	C₁₃≀C₂	C13wrC2	C13xD13	26	2	338,3

Groups of order 375

		Label	Label	d	ρ	ID
C₅×C₅²⋊C₃	C₅≀C₃	C5wrC3	C5xC5^2:C3	15	3	375,6

Groups of order 392

		Label	Label	d	ρ	ID
C₇×C₇⋊D₄	C₁₄≀C₂	C14wrC2	C7xC7:D4	28	2	392,27
D₇≀C₂	D₇≀C₂	D7wrC2	D7wrC2	14	4+	392,37

Groups of order 450

		Label	Label	d	ρ	ID
C₁₅×D₁₅	C₁₅≀C₂	C15wrC2	C15xD15	30	2	450,29

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