Finite Group Databasebeta

C22×#11718565 #16769406

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

Aliases

direct productC22×#11718565

Splittings

FittingC23×C13×C16 ⋊ C2
SylowC13 ⋊ C22×#508

Subgroups

subgroupG/H
centerC22×C4D104
commutator, cosocleC8×C13C25
FrattiniC8C24×D13
FittingC23×C13×C16C2
socleC23×C13C2×D8
hypercenterC23×C16D13
hypocenterC13C22×#508
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8 ◁ C23×C16

2118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1076055);