Finite Group Databasebeta

C4×#11719496 #16021382

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#11719496

Splittings

FittingC23×C42×C13 ⋊ C2
SylowC13 ⋊ C4×#525

Subgroups

subgroupG/H
centerC2×C42C22×D13
commutatorC22×C13C24×C4
FrattiniC23C24×D13
FittingC23×C42×C13C2
socle, cosocleC23×C13C25
prime radicalC2×#11719496C2
hypercenterC23×C42D13
hypocenterC13C4×#525
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C42 ◁ C23×C42

3902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 328031);