Finite Group Databasebeta

#261×#364 #16789572

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

Aliases

direct product#261×#364

Splittings

FittingC13×#364 ⋊ C4
SylowC13 ⋊ C4×#364

Subgroups

subgroupG/H
centerC8D4×#261
commutatorC4×C13C2×C4×C8
FrattiniC2×C8C22×#261
FittingC13×#364C4
socleC2×C13C4×C4⋊C8
prime radicalC22×D13C2×M16
cosocleC2×C8×D13C23
hypercenter#364#261
hypocenterC13C4×#364
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C8 ◁ #364

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

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, 1096221);