Finite Group Databasebeta

C22×#11718572 #16769409

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

Aliases

direct productC22×#11718572

Splittings

FittingC22×C13×D16 ⋊ C2
SylowC13 ⋊ C22×#509

Subgroups

subgroupG/H
centerC23D8×D13
commutator, cosocleC8×C13C25
FrattiniC8C24×D13
FittingC22×C13×D16C2
socleC23×C13C2×D8
hypercenterC22×D16D13
hypocenterC13C22×#509
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

2334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076058);