Finite Group Databasebeta

C22×#11719153 #16808096

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

Aliases

direct productC22×#11719153
unambiguous semidirect productD13⋊(C2×#419)

Splittings

FittingC23×Q8×C13 ⋊ C4
SylowC13 ⋊ C22×#419

Subgroups

subgroupG/H
centerC23C2×C22⋊#261
commutatorC4×C13C24×C4
FrattiniC4C24×#261
FittingC23×Q8×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC24×D13D4
cosocleC4×D13C25
hypercenterC23×Q8#261
hypocenterC13C22×#419
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q8

5070 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1114745);