Finite Group Databasebeta

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C23×#13063248 #25960108

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×#13063248

Splittings

SylowC43 ⋊ C23×#103

Subgroups

subgroupG/H
centerC25C22⋊D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC23×C4⋊C4×C43C2
socle, prime radicalC25×C43D4
cosocleC2×C4×C43C25
hypercenterC23×C4⋊C4D43
hypocenterC43C23×#103
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

5502 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033079);