Finite Group Databasebeta

C2×C4×#15668426 #37536052

order23168
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#15668426

Splittings

FittingC22×C42×C181 ⋊ C2
SylowC181 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D181
commutatorC2×C181C22×C42
FrattiniC23C23×D181
FittingC22×C42×C181C2
socleC24×C181C23
prime radicalC24×D181C22
cosocleC23×C181C24
hypercenterC22×C42D181
hypocenterC181C2×C4×C22⋊C4
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 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, 6841);