Finite Group Databasebeta

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C4×#14583328 #25249874

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#14583328

Splittings

FittingC4×D16×C43 ⋊ C2
SylowC43 ⋊ C4×#508

Subgroups

subgroupG/H
centerC2×C4D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC4×D16×C43C2
socleC22×C43C22×D8
prime radicalC2×#14583328C2
cosocleC2×C8×C43C24
hypercenterC4×D16D43
hypocenterC43C4×#508
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D16

690 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322845);