Finite Group Databasebeta

C22×#1057⋊C8 #16792565

order3328
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×#1057⋊C8

Splittings

SylowC13 ⋊ C22×#322

Subgroups

subgroupG/H
centerC23×C4C2×#261
commutatorC2×C13C22×C4×C8
FrattiniC2×C4C23×#261
FittingC23×C8×C13C4
socle, prime radicalC24×C13C42
cosocleC4×Dic13C24
hypercenterC23×C8#261
hypocenterC13C22×#322
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C23×C8

1182 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, 1099214);