Finite Group Databasebeta

C22×#11718350 #16726309

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×#11718350

Splittings

FittingC22×C4×C8×C13 ⋊ C2
SylowC13 ⋊ C22×#405

Subgroups

subgroupG/H
centerC23×C8C2×D13
commutatorC2×C13C23×C42
FrattiniC2×C4C24×D13
FittingC22×C4×C8×C13C2
socleC24×C13C22×C4
prime radicalC24×D13C2×C4
cosocleC2×C4×C13C25
hypercenterC22×C4×C8D13
hypocenterC13C22×#405
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

3518 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, 1032958);