Finite Group Databasebeta

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C4×#14583263 #25104668

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

Aliases

direct productC4×#14583263

Splittings

SylowC43 ⋊ C4×#490

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#127×C43C2
socleC23×C43C22×D4
prime radicalC2×#127×C43C22
cosocleC22×C4×C43C24
hypercenterC4×#127D43
hypocenterC43C4×#490
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#127

970 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 177639);