Finite Group Databasebeta

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C2×#10593453 #11801330

order1152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#10593453

Splittings

FittingC22×C32×C4 ⋊ D4
SylowC32 ⋊ C2×#386

Subgroups

subgroupG/H
centerC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC23×C32C2×D4
prime radicalC23×GO+(4,𝔽2)C2
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#386
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

2594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 35341);