Finite Group Databasebeta

C23×#13063252 #25960185

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

Aliases

direct productC23×#13063252

Splittings

SylowC43 ⋊ C23×#104

Subgroups

subgroupG/H
centerC23×C4C22⋊D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
Fitting, prime radicalC23×#41×C43C2
socleC24×C43C22⋊C4
cosocleC2×C4×C43C25
hypercenterC23×#41D43
hypocenterC43C23×#104
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C23×#41

5758 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, 1033156);