Finite Group Databasebeta

C22×#11718808 #16769411

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

Aliases

direct productC22×#11718808

Splittings

FittingC23×C13×D8 ⋊ C2
SylowC13 ⋊ C22×#509

Subgroups

subgroupG/H
centerC23C2×#6104
commutator, cosocleC8×C13C25
FrattiniC8C24×D13
FittingC23×C13×D8C2
socleC23×C13C2×D8
hypercenterC23×D8D13
hypocenterC13C22×#509
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C23×D8

2334 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, 1076060);