Finite Group Databasebeta

#261×#349 #16789303

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

Aliases

direct product#261×#349

Splittings

FittingC13×#349 ⋊ C4
SylowC13 ⋊ C4×#349

Subgroups

subgroupG/H
centerC4C22⋊C4×#261
commutatorC22×C13C2×C4×C8
FrattiniC2×C8C22×#261
FittingC13×#349C4
socleC2×C13C4×C22⋊C8
prime radicalC23×D13C2×C8
cosocleC2×C8×D13C23
hypercenter#349#261
hypocenterC13C4×#349
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ #349

522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

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, 1095952);