Finite Group Databasebeta

C22×#11718290 #16796743

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C28

Aliases

direct productC22×#11718290

Splittings

SylowC13 ⋊ C22×#336

Subgroups

subgroupG/H
centerC25C2×#261
commutatorC2×C13C22×C4×C8
FrattiniC23C23×#261
FittingC24×C4×C13C4
socle, prime radicalC25×C13C2×C4
cosocleC22×Dic13C24
hypercenterC24×C4#261
hypocenterC13C22×#336
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C25 ◁ C24×C4

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1103392);