Finite Group Databasebeta

C22×(C2×#261)⋊C8 #16796742

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C28

Aliases

direct productC22×(C2×#261)⋊C8

Splittings

FittingC23×C8×C13 ⋊ C4
SylowC13 ⋊ C22×#336

Subgroups

subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C22×C4×C8
FrattiniC2×C4C23×#261
FittingC23×C8×C13C4
socleC24×C13C42
prime radicalC24×D13C2×C4
cosocleC2×C4×D13C24
hypercenterC23×C8#261
hypocenterC13C22×#336
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C23×C8

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103391);