Finite Group Databasebeta

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C4×#14582908 #25094381

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#14582908

Splittings

SylowC43 ⋊ C4×#419

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC22×C4×Q8×C43C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC22×C4×Q8D43
hypocenterC43C4×#419
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×Q8

1586 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, 167352);