Finite Group Databasebeta

C22×#11718494 #16726625

order3328
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×#11718494

Splittings

FittingC22×C13×C4⋊C8 ⋊ C2
SylowC13 ⋊ C22×#431

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC2×C13C24×C8
FrattiniC2×C4C24×D13
FittingC22×C13×C4⋊C8C2
socleC24×C13C22×C4
prime radicalC24×D13C2×C4
cosocleC2×C4×C13C25
hypercenterC22×C4⋊C8D13
hypocenterC13C22×#431
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

3086 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033274);