Finite Group Databasebeta

#261×#332 #16780711

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#261×#332

Splittings

FittingC13×#332 ⋊ C4
SylowC13 ⋊ C4×#332

Subgroups

subgroupG/H
centerC22C22⋊C4×#261
commutatorC2×C4×C13C2×C42
FrattiniC42C22×#261
FittingC13×#332C4
socleC22×C13C4×C22⋊C4
prime radicalC22×D13C2×C22⋊C4
cosocleC42×D13C23
hypercenter#332#261
hypocenterC13C4×#332
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #332

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

133 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1087360);