Finite Group Databasebeta

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C23×#13063245 #25960104

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×#13063245

Splittings

FittingC23×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ C23×#102

Subgroups

subgroupG/H
centerC25C22⋊D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC23×C4⋊C4×C43C2
socleC25×C43D4
prime radicalC24×D172C2
cosocleC2×C4×C43C25
hypercenterC23×C4⋊C4D43
hypocenterC43C23×#102
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

7646 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, 1033075);