Finite Group Databasebeta

C22×#11718600 #16021271

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×#11718600

Splittings

FittingC23×C42×C13 ⋊ C2
SylowC13 ⋊ C22×#390

Subgroups

subgroupG/H
centerC25C22×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC23×C42×C13C2
socleC25×C13C23
prime radicalC24×D52C2
cosocleC23×C13C25
hypercenterC23×C42D13
hypocenterC13C22×#390
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C25 ◁ C23×C42

9534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 327920);