Finite Group Databasebeta

#261×#488 #16800307

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

Aliases

direct product#261×#488

Splittings

FittingC13×#488 ⋊ C4
SylowC13 ⋊ C4×#488

Subgroups

subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#488C4
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C23
cosocleC2×C4×D13C24
hypercenter#488#261
hypocenterC13C4×#488
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #488

858 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, 1106956);