Finite Group Databasebeta

C23×#13063247 #25960106

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

Aliases

direct productC23×#13063247

Splittings

FittingC24×C8×C43 ⋊ C2
SylowC43 ⋊ C23×#102

Subgroups

subgroupG/H
centerC25D172
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC24×C8×C43C2
socleC25×C43D4
prime radicalC24×D172C2
cosocleC2×C4×C43C25
hypercenterC24×C8D43
hypocenterC43C23×#102
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C25 ◁ C24×C4 ◁ C24×C8

7646 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, 1033077);