Finite Group Databasebeta

C22×#11718579 #16769418

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

Aliases

direct productC22×#11718579

Splittings

FittingC22×C13×Q32 ⋊ C2
SylowC13 ⋊ C22×#510

Subgroups

subgroupG/H
centerC23D8×D13
commutator, cosocleC8×C13C25
FrattiniC8C24×D13
FittingC22×C13×Q32C2
socleC23×C13C2×D8
prime radicalC22×#88173C2
hypercenterC22×Q32D13
hypocenterC13C22×#510
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

2078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

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, 1076067);