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Cayley diagram

C2×#3792 #64292

order288
isoclinismisoclinic class of #3788
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3

Aliases

direct productC2×#3792

Splittings

SylowC32 ⋊ C2×M16

Subgroups

subgroupG/H
centerC22C2×#157
commutatorC2×C32C22×C4
FrattiniC2C22×#157
Fitting, prime radicalC23×C32C4
socleC22×C32C2×C4
cosocleC3⋊Dic3C23
hypercenterC23#157
hypocenterC32C2×M16
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23

122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 48

A minimal faithful permutation representation — 3 generators on 16 points:

(1,2)(3,7,5)(10,13)(14,16);(3,4)(5,6,7,8)(9,10,11,14,12,13,15,16);(1,2)

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10590073, #10590074, #10590096, …
maximal normal subgroup of#10590073, #10590074, #10590096, …
maximal quotient ofC2×#63777, C4×#3792, C2×#63779, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 940);