Finite Group Databasebeta

C22×#11718794 #16726454

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

Aliases

direct productC22×#11718794

Splittings

FittingC23×C13×M16 ⋊ C2
SylowC13 ⋊ C22×#417

Subgroups

subgroupG/H
centerC24C2×D52
commutatorC4×C13C24×C4
FrattiniC2×C4C24×D13
FittingC23×C13×M16C2
socleC24×C13C2×D4
prime radicalC23×#6127C2
cosocleC2×C4×C13C25
hypercenterC23×M16D13
hypocenterC13C22×#417
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×M16

5502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1664

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1033103);