Finite Group Databasebeta

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C2×#19137200 #25255188

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#19137200

Splittings

FittingC2×C4×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ C2×#2314

Subgroups

subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C4×C4⋊C4×C43C2
socleC24×C43C24
prime radicalC24×D43C23
cosocleC23×C43C25
hypercenterC2×C4×C4⋊C4D43
hypocenterC43C2×#2314
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

2678 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 328159);