Finite Group Databasebeta

C22×#19153756 #37546817

order23168
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×#19153756

Splittings

SylowC181 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C8C2×D181
commutatorC2×C181C23×C8
FrattiniC8C23×D181
FittingC23×C8×C181C2
socleC23×C181C2×C8
prime radicalC24×C181C8
cosocleC8×C181C24
hypercenterC23×C8D181
hypocenterC181C22×M32
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C22×C8 ◁ C23×C8

400 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, 17606);