Finite Group Databasebeta

#261×#520 #16807462

order3328
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct product#261×#520

Splittings

FittingC13×#520 ⋊ C4
SylowC13 ⋊ C4×#520

Subgroups

subgroupG/H
center, FrattiniC22C24×#261
commutatorC2×C13C23×C42
FittingC13×#520C4
socleC22×C13C24×C4
prime radicalC2×#41×D13C22
cosocleC22×D13C25
hypercenter#520#261
hypocenterC13C4×#520
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #520

3698 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114111);