Wreath products

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

H ≀ S = Hn ⋊ S
where S acts on Hn via S⊆Sn, permuting the n copies of H.

Groups of order 8

LabelLabeldρID
D4C2≀C2C2wrC2D442+8,3

Groups of order 18

LabelLabeldρID
C3×S3C3≀C2C3wrC2C3xS36218,3

Groups of order 24

LabelLabeldρID
C2×A4C2≀C3C2wrC3C2xA463+24,13

Groups of order 32

LabelLabeldρID
C4≀C2C4≀C2C4wrC2C4wrC28232,11
C22≀C2C22≀C2C2^2wrC2C2^2wrC2832,27

Groups of order 48

LabelLabeldρID
C2×S4C2≀S3C2wrS3C2xS463+48,48

Groups of order 50

LabelLabeldρID
C5×D5C5≀C2C5wrC2C5xD510250,3

Groups of order 64

LabelLabeldρID
C2≀C4C2≀C4C2wrC4C2wrC484+64,32
C2≀C22C2≀C22C2wrC2^2C2wrC2^284+64,138

Groups of order 72

LabelLabeldρID
C3×C3⋊D4C6≀C2C6wrC2C3xC3:D412272,30
S3≀C2S3≀C2S3wrC2S3wrC264+72,40

Groups of order 81

LabelLabeldρID
C3≀C3C3≀C3C3wrC3C3wrC39381,7

Groups of order 98

LabelLabeldρID
C7×D7C7≀C2C7wrC2C7xD714298,3

Groups of order 128

LabelLabeldρID
C8≀C2C8≀C2C8wrC2C8wrC2162128,67
(C2×C4)≀C2(C2×C4)≀C2(C2xC4)wrC2(C2xC4)wrC216128,628
C2≀D4C2≀D4C2wrD4C2wrD484+128,928
D4≀C2D4wrC2
Q8≀C2Q8≀C2Q8wrC2Q8wrC2164-128,937
C23≀C2C23≀C2C2^3wrC2C2^3wrC216128,1578

Groups of order 160

LabelLabeldρID
C2×C24⋊C5C2≀C5C2wrC5C2xC2^4:C5105+160,235

Groups of order 162

LabelLabeldρID
C9×D9C9≀C2C9wrC2C9xD9182162,3
C3≀S3C3≀S3C3wrS3C3wrS393162,10
C32×C3⋊S3C32≀C2C3^2wrC2C3^2xC3:S318162,52

Groups of order 192

LabelLabeldρID
C4×C42⋊C3C4≀C3C4wrC3C4xC4^2:C3123192,188
C2≀A4C2≀A4C2wrA4C2wrA484+192,201
C22×C22⋊A4C22≀C3C2^2wrC3C2^2xC2^2:A412192,1540

Groups of order 200

LabelLabeldρID
C5×C5⋊D4C10≀C2C10wrC2C5xC5:D4202200,31
D5≀C2D5≀C2D5wrC2D5wrC2104+200,43

Groups of order 242

LabelLabeldρID
C11×D11C11≀C2C11wrC2C11xD11222242,3

Groups of order 288

LabelLabeldρID
C3×C424S3C12≀C2C12wrC2C3xC4^2:4S3242288,239
Dic3≀C2Dic3≀C2Dic3wrC2Dic3wrC2244-288,389
C3×C244S3(C2×C6)≀C2(C2xC6)wrC2C3xC2^4:4S324288,724
D6≀C2D6≀C2D6wrC2D6wrC2124+288,889
A4≀C2A4≀C2A4wrC2A4wrC286+288,1025

Groups of order 320

LabelLabeldρID
C2×C24⋊D5C2≀D5C2wrD5C2xC2^4:D5105+320,1636

Groups of order 324

LabelLabeldρID
C3×C33⋊C4C3≀C4C3wrC4C3xC3^3:C4124324,162
C3×C324D6C3≀C22C3wrC2^2C3xC3^2:4D6124324,167

Groups of order 338

LabelLabeldρID
C13×D13C13≀C2C13wrC2C13xD13262338,3

Groups of order 375

LabelLabeldρID
C5×C52⋊C3C5≀C3C5wrC3C5xC5^2:C3153375,6

Groups of order 392

LabelLabeldρID
C7×C7⋊D4C14≀C2C14wrC2C7xC7:D4282392,27
D7≀C2D7≀C2D7wrC2D7wrC2144+392,37

Groups of order 450

LabelLabeldρID
C15×D15C15≀C2C15wrC2C15xD15302450,29
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