Finite Group Databasebeta

C4×#11719089 #16796733

order3328
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C22×C43

Aliases

direct productC4×#11719089

Splittings

FittingC2×C4×C8×C13 ⋊ C4
SylowC13 ⋊ C4×#405

Subgroups

subgroupG/H
centerC4×C8C2×#261
commutatorC2×C13C2×C43
FrattiniC2×C4C23×#261
FittingC2×C4×C8×C13C4
socleC22×C13C22×C42
prime radicalC23×D13C22×C4
cosocleC2×C4×D13C24
hypercenterC2×C4×C8#261
hypocenterC13C4×#405
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C4×C8 ◁ C2×C4×C8

1526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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(3328, 1103382);