Finite Group Databasebeta

C22×#11718046 #15828488

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

Aliases

direct productC22×#11718046

Splittings

SylowC13 ⋊ C22×#322

Subgroups

subgroupG/H
centerC22×C42C2×D13
commutatorC2×C13C22×C4×C8
FrattiniC42C23×D13
FittingC22×C4×C8×C13C2
socle, prime radicalC24×C13C42
cosocleC42×C13C24
hypercenterC22×C4×C8D13
hypocenterC13C22×#322
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C42 ◁ C22×C4×C8

1182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3328

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 135137);