Wreath products

If H and S⊆Sn 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⊆Sn, permuting the n copies of H.

Groups of order 8

LabelLabeldρID
D4C2wrC2C2wrC2D442+8,3

Groups of order 18

LabelLabeldρID
C3xS3C3wrC2C3wrC2C3xS36218,3

Groups of order 24

LabelLabeldρID
C2xA4C2wrC3C2wrC3C2xA463+24,13

Groups of order 32

LabelLabeldρID
C4wrC2C4wrC2C4wrC2C4wrC28232,11
C22wrC2C22wrC2C2^2wrC2C2^2wrC2832,27

Groups of order 48

LabelLabeldρID
C2xS4C2wrS3C2wrS3C2xS463+48,48

Groups of order 50

LabelLabeldρID
C5xD5C5wrC2C5wrC2C5xD510250,3

Groups of order 64

LabelLabeldρID
C2wrC4C2wrC4C2wrC4C2wrC484+64,32
C2wrC22C2wrC22C2wrC2^2C2wrC2^284+64,138

Groups of order 72

LabelLabeldρID
C3xC3:D4C6wrC2C6wrC2C3xC3:D412272,30
S3wrC2S3wrC2S3wrC2S3wrC264+72,40

Groups of order 81

LabelLabeldρID
C3wrC3C3wrC3C3wrC3C3wrC39381,7

Groups of order 98

LabelLabeldρID
C7xD7C7wrC2C7wrC2C7xD714298,3

Groups of order 128

LabelLabeldρID
C8wrC2C8wrC2C8wrC2C8wrC2162128,67
(C2xC4)wrC2(C2xC4)wrC2(C2xC4)wrC2(C2xC4)wrC216128,628
D4wrC2D4wrC2D4wrC2D4wrC284+128,928
C2wrD4C2wrD4
Q8wrC2Q8wrC2Q8wrC2Q8wrC2164-128,937
C23wrC2C23wrC2C2^3wrC2C2^3wrC216128,1578

Groups of order 160

LabelLabeldρID
C2xC24:C5C2wrC5C2wrC5C2xC2^4:C5105+160,235

Groups of order 162

LabelLabeldρID
C9xD9C9wrC2C9wrC2C9xD9182162,3
C3wrS3C3wrS3C3wrS3C3wrS393162,10
C32xC3:S3C32wrC2C3^2wrC2C3^2xC3:S318162,52

Groups of order 192

LabelLabeldρID
C4xC42:C3C4wrC3C4wrC3C4xC4^2:C3123192,188
C2wrA4C2wrA4C2wrA4C2wrA484+192,201
C22xC22:A4C22wrC3C2^2wrC3C2^2xC2^2:A412192,1540

Groups of order 200

LabelLabeldρID
C5xC5:D4C10wrC2C10wrC2C5xC5:D4202200,31
D5wrC2D5wrC2D5wrC2D5wrC2104+200,43

Groups of order 242

LabelLabeldρID
C11xD11C11wrC2C11wrC2C11xD11222242,3

Groups of order 288

LabelLabeldρID
C3xC42:4S3C12wrC2C12wrC2C3xC4^2:4S3242288,239
Dic3wrC2Dic3wrC2Dic3wrC2Dic3wrC2244-288,389
C3xC24:4S3(C2xC6)wrC2(C2xC6)wrC2C3xC2^4:4S324288,724
D6wrC2D6wrC2D6wrC2D6wrC2124+288,889
A4wrC2A4wrC2A4wrC2A4wrC286+288,1025

Groups of order 320

LabelLabeldρID
C2xC24:D5C2wrD5C2wrD5C2xC2^4:D5105+320,1636

Groups of order 324

LabelLabeldρID
C3xC33:C4C3wrC4C3wrC4C3xC3^3:C4124324,162
C3xC32:4D6C3wrC22C3wrC2^2C3xC3^2:4D6124324,167

Groups of order 338

LabelLabeldρID
C13xD13C13wrC2C13wrC2C13xD13262338,3

Groups of order 375

LabelLabeldρID
C5xC52:C3C5wrC3C5wrC3C5xC5^2:C3153375,6

Groups of order 392

LabelLabeldρID
C7xC7:D4C14wrC2C14wrC2C7xC7:D4282392,27
D7wrC2D7wrC2D7wrC2D7wrC2144+392,37

Groups of order 450

LabelLabeldρID
C15xD15C15wrC2C15wrC2C15xD15302450,29
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