Finite Group Databasebeta

C2×C4×#14268659 #28407726

order14464
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×#14268659

Splittings

derived, SylowC113 ⋊ C2×C4×C16

Subgroups

subgroupG/H
center, hypercenterC22×C4#11744762
commutator, hypocenterC113C2×C4×C16
FrattiniC22C22×#11744762
FittingC22×C4×C113C8
socle, prime radicalC23×C113C2×C8
cosocleC2×#11744753C23
LCSG ▷ C113
UCSC1 ◁ C22×C4

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14464

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21662);