Finite Group Databasebeta

C4×#11718666 #15860643

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#11718666

Splittings

FittingC4×C13×#117 ⋊ C2
SylowC13 ⋊ C4×#421

Subgroups

subgroupG/H
centerC42C2×D52
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC4×C13×#117C2
socleC22×C13C22×C22⋊C4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenterC4×#117D13
hypocenterC13C4×#421
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C42 ◁ C22×C42 ◁ C4×#117

1618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 167292);