Finite Group Databasebeta

#261×#525 #16807493

order3328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product#261×#525

Splittings

FittingC13×#525 ⋊ C4
SylowC13 ⋊ C4×#525

Subgroups

subgroupG/H
centerC2×C4C23×#261
commutator, socleC22×C13C24×C4
FrattiniC22C24×#261
FittingC13×#525C4
prime radicalD13×#525C2
cosocleC22×D13C25
hypercenter#525#261
hypocenterC13C4×#525
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #525

3902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#261×#3484
maximal normal subgroup of#261×#3484

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1114142);