Finite Group Databasebeta

C22×#11718771 #16726353

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#11718771

Splittings

FittingC24×C8×C13 ⋊ C2
SylowC13 ⋊ C22×#408

Subgroups

subgroupG/H
centerC23×C4C22×D13
commutatorC22×C13C24×C4
FrattiniC2×C4C24×D13
FittingC24×C8×C13C2
socleC24×C13C22×C4
prime radicalC23×#6127C2
cosocleC2×C4×C13C25
hypercenterC24×C8D13
hypocenterC13C22×#408
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C24×C8

5326 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033002);