Finite Group Databasebeta

C22×#11718087 #16015869

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#11718087

Splittings

FittingC22×C13×#108 ⋊ C2
SylowC13 ⋊ C22×#361

Subgroups

subgroupG/H
centerC23#88049
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
FittingC22×C13×#108C2
socleC23×C13#102
prime radicalC23×D104C2
cosocleC2×C8×C13C24
hypercenterC22×#108D13
hypocenterC13C22×#361
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C22×#108

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 322518);