Finite Group Databasebeta

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C4×#14583317 #25249243

order11008
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#14583317

Splittings

FittingC4×M32×C43 ⋊ C2
SylowC43 ⋊ C4×#504

Subgroups

subgroupG/H
centerC4×C8C22×D43
commutatorC2×C43C22×C4×C8
FrattiniC2×C8C23×D43
FittingC4×M32×C43C2
socleC22×C43C23×C8
prime radicalC2×#10621898C2×C4
cosocleC2×C8×C43C24
hypercenterC4×M32D43
hypocenterC43C4×#504
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C4×C8 ◁ C4×M32

834 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322214);