Finite Group Databasebeta

C22×#11719073 #16808248

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11719073

Splittings

SylowC13 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC24C22×#261
commutatorC2×C13C24×C8
FrattiniC22C24×#261
FittingC22×C13×C4⋊C4C4
socleC24×C13C22×C4
prime radicalC23×D52C4
cosocleC2×Dic13C25
hypercenterC22×C4⋊C4#261
hypocenterC13C22×C8×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4⋊C4

3694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114897);