Finite Group Databasebeta

C23×#13063261 #25960286

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC23×#13063261

Splittings

SylowC43 ⋊ C23×#108

Subgroups

subgroupG/H
centerC23×C4D172
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC24×C8×C43C2
socleC24×C43C4⋊C4
prime radicalC25×C43Q8
cosocleC2×C4×C43C25
hypercenterC24×C8D43
hypocenterC43C23×#108
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C24×C8

2846 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033257);