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Cayley diagram

C2×#3774 #64235

order288
isoclinismisoclinic class of #3774
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productC2×#3774

Splittings

SylowC32 ⋊ C2×D8

Subgroups

subgroupG/H
center, hypercenterC22GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C23
FrattiniC2C2×GO+(4,𝔽2)
Fitting, socleC22×C32D4
hypocenterC32C2×D8
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22

130 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:

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

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#10593168, C4×#3774, #10593417, …
maximal normal subgroup of#10593168, C4×#3774, #10593417, …
maximal quotient ofC2×#63734, #10593333, #10593334, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 883);