Finite Group Databasebeta

C22×#11718271 #16796812

order3328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11718271

Splittings

FittingC22×C13×M16 ⋊ C4
SylowC13 ⋊ C22×#343

Subgroups

subgroupG/H
centerC23(C2×#261)⋊C4
commutatorC22×C13C22×C42
FrattiniC2×C4C23×#261
FittingC22×C13×M16C4
socleC23×C13#95
prime radicalC24×D13C2×C4
cosocleC2×C4×D13C24
hypercenterC22×M16#261
hypocenterC13C22×#343
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

2494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103461);