Finite Group Databasebeta

C22×#11718154 #16015791

order3328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#11718154

Splittings

SylowC13 ⋊ C22×#357

Subgroups

subgroupG/H
centerC24#6104
commutatorC8×C13C23×C4
FrattiniC2×C8C23×D13
Fitting, prime radicalC23×C13×D8C2
socleC24×C13D8
cosocleC2×C8×C13C24
hypercenterC23×D8D13
hypocenterC13C22×#357
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8 ◁ C23×D8

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 322440);