Finite Group Databasebeta

C2×C4×#15668433 #37542130

order23168
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C4×#15668433

Splittings

SylowC181 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC2×C42C2×D181
commutatorC2×C181C22×C42
FrattiniC2×C4C23×D181
FittingC22×C42×C181C2
socleC23×C181C22×C4
prime radicalC24×C181C2×C4
cosocleC2×C4×C181C24
hypercenterC22×C42D181
hypocenterC181C2×C4×M16
LCSG ▷ C2×C181 ▷ C181
UCSC1 ◁ C2×C42 ◁ C22×C42

656 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, 12919);