Finite Group Databasebeta

C2×#26041331 #37542336

order23168
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#26041331

Splittings

FittingC2×C4⋊C8×C181 ⋊ C2
SylowC181 ⋊ C2×#431

Subgroups

subgroupG/H
centerC22×C4C22×D181
commutatorC2×C181C23×C8
FrattiniC2×C4C23×D181
FittingC2×C4⋊C8×C181C2
socleC23×C181C22×C4
prime radicalC23×D181C2×C4
cosocleC2×C4×C181C24
hypercenterC2×C4⋊C8D181
hypocenterC181C2×#431
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C22×C4 ◁ C2×C4⋊C8

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11584

Conjugacy classes & character table

3680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23168, 13125);