Finite Group Databasebeta

C22×#11718562 #16769382

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11718562

Splittings

FittingC23×C13×C16 ⋊ C2
SylowC13 ⋊ C22×#504

Subgroups

subgroupG/H
centerC22×C16C2×D13
commutatorC2×C13C24×C8
FrattiniC8C24×D13
FittingC23×C13×C16C2
socleC23×C13C22×C8
prime radicalC22×#6127C4
cosocleC8×C13C25
hypercenterC23×C16D13
hypocenterC13C22×#504
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C16 ◁ C23×C16

2118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076031);