Finite Group Databasebeta

#261×#324 #16780358

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct product#261×#324

Splittings

FittingC13×#324 ⋊ C4
SylowC13 ⋊ C4×#324

Subgroups

subgroupG/H
centerC22C22⋊C4×#261
commutatorC22×C13C2×C4×C8
FrattiniC22×C4C22×#261
FittingC13×#324C4
socleC22×C13C4×C22⋊C4
prime radicalC23×D13C22×C4
cosocleC22×C4×D13C23
hypercenter#324#261
hypocenterC13C4×#324
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1087007);