Finite Group Databasebeta

#261×#358 #16789494

order3328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#261×#358

Splittings

FittingC13×#358 ⋊ C4
SylowC13 ⋊ C4×#358

Subgroups

subgroupG/H
centerC22D8×#261
commutatorC8×C13C2×C42
FrattiniC2×C8C22×#261
FittingC13×#358C4
socleC22×C13C4×D8
prime radicalC22×D13C2×D8
cosocleC2×C8×D13C23
hypercenter#358#261
hypocenterC13C4×#358
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

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, 1096143);