Finite Group Databasebeta

C23×#15668432 #37548422

order23168
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC23×#15668432

Splittings

FittingC23×C8×C181 ⋊ C2
SylowC181 ⋊ C23×M16

Subgroups

subgroupG/H
centerC23×C4C2×D181
commutatorC2×C181C24×C4
FrattiniC4C24×D181
FittingC23×C8×C181C2
socleC24×C181C2×C4
prime radicalC24×D181C4
cosocleC4×C181C25
hypercenterC23×C8D181
hypocenterC181C23×M16
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C23×C4 ◁ C23×C8

1720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11584

Conjugacy classes & character table

5840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 19211);