Finite Group Databasebeta

C4×#11719151 #16791544

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

Aliases

direct productC4×#11719151

Splittings

FittingC2×C4×D4×C13 ⋊ C4
SylowC13 ⋊ C4×#390

Subgroups

subgroupG/H
centerC22×C4C22×#261
commutatorC22×C13C22×C42
FrattiniC23C23×#261
FittingC2×C4×D4×C13C4
socleC23×C13C23×C4
prime radicalC22×D4×D13C22
cosocleC23×D13C24
hypercenterC2×C4×D4#261
hypocenterC13C4×#390
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

2894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

232 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1098193);