Finite Group Databasebeta

#261×#334 #16780911

order3328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#261×#334

Splittings

FittingC13×#334 ⋊ C4
SylowC13 ⋊ C4×#334

Subgroups

subgroupG/H
centerC2×C4D4×#261
commutatorC4×C13C2×C4×C8
FrattiniC42C22×#261
FittingC13×#334C4
socleC22×C13C4×C4⋊C4
prime radicalC22×D13C2×C4⋊C4
cosocleC42×D13C23
hypercenter#334#261
hypocenterC13C4×#334
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C42 ◁ #334

470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 832

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1087560);