Finite Group Databasebeta

C22×#11718659 #16726567

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×#11718659

Splittings

SylowC13 ⋊ C22×#427

Subgroups

subgroupG/H
centerC23×C4C22⋊D13
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC22×C13×#117C2
socleC24×C13C2×D4
prime radicalC25×C13D4
cosocleC2×C4×C13C25
hypercenterC22×#117D13
hypocenterC13C22×#427
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C22×#117

3006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033216);