Finite Group Databasebeta

C4×#11718091 #15783096

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#11718091

Splittings

SylowC13 ⋊ C4×M64

Subgroups

subgroupG/H
centerC4×C16C2×D13
commutatorC2×C13C2×C4×C16
FrattiniC2×C16C22×D13
FittingC2×C4×C13×C16C2
socleC22×C13C22×C16
prime radicalC23×C13C2×C16
cosocleC2×C13×C16C23
hypercenterC2×C4×C16D13
hypocenterC13C4×M64
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C16 ◁ C2×C4×C16

250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 89745);