Finite Group Databasebeta

C22×#11718853 #16730303

order3328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#11718853

Splittings

FittingC23×C13×Q16 ⋊ C2
SylowC13 ⋊ C22×#473

Subgroups

subgroupG/H
centerC23#88192
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC23×C13×Q16C2
socleC23×C13#121
prime radicalC22×#6127C22
hypercenterC23×Q16D13
hypocenterC13C22×#473
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

2630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1036952);