Finite Group Databasebeta

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C4×#14582622 #24987100

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#14582622

Splittings

FittingC4×C22⋊C8×C43 ⋊ C2
SylowC43 ⋊ C4×#323

Subgroups

subgroupG/H
centerC22×C4(C2×D43)⋊C4
commutatorC22×C43C2×C4×C8
FrattiniC23×C4C22×D43
FittingC4×C22⋊C8×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenterC4×C22⋊C8D43
hypocenterC43C4×#323
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

946 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, 60071);