Finite Group Databasebeta

C2×#26041342 #37542391

order23168
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×#26041342

Splittings

FittingC2×C22⋊C8×C181 ⋊ C2
SylowC181 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×D181
commutatorC2×C181C23×C8
FrattiniC2×C4C23×D181
FittingC2×C22⋊C8×C181C2
socleC23×C181C22×C4
prime radicalC22×C22⋊D181C4
cosocleC2×C4×C181C24
hypercenterC2×C22⋊C8D181
hypocenterC181C2×C8×D4
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

616 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, 13180);