Finite Group Databasebeta

#261×#533 #16807501

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#261×#533

Splittings

FittingC13×#533 ⋊ C4
SylowC13 ⋊ C4×#533

Subgroups

subgroupG/H
centerC2×C4C23×#261
commutator, socleC22×C13C24×C4
FrattiniC22C24×#261
FittingC13×#533C4
prime radicalC23×D13C24
cosocleC22×D13C25
hypercenter#533#261
hypocenterC13C4×#533
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #533

2550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 416

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, 1114150);