Finite Group Databasebeta

C23×#13063241 #25960078

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

Aliases

direct productC23×#13063241

Splittings

FittingC23×M16×C43 ⋊ C2
SylowC43 ⋊ C23×#100

Subgroups

subgroupG/H
centerC24(C2×D43)⋊C4
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC23×M16×C43C2
socleC24×C43C22⋊C4
prime radicalC24×D172C2
cosocleC2×C4×C43C25
hypercenterC23×M16D43
hypocenterC43C23×#100
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×M16

7134 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033049);