Finite Group Databasebeta

C22×#11718144 #15860336

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

Aliases

direct productC22×#11718144

Splittings

SylowC13 ⋊ C22×#341

Subgroups

subgroupG/H
centerC23×C4D52
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC24×C8×C13C2
socleC24×C13C4⋊C4
prime radicalC25×C13Q8
cosocleC22×C4×C13C24
hypercenterC24×C8D13
hypocenterC13C22×#341
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C24×C8

2238 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, 166985);