Finite Group Databasebeta

#261×#546 #16807619

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

Aliases

direct product#261×#546

Splittings

FittingC13×#546 ⋊ C4
SylowC13 ⋊ C4×#546

Subgroups

subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#546C4
prime radicalD13×#546C2
cosocleC22×D13C25
hypercenter#546#261
hypocenterC13C4×#546
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #546

3720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 208

Conjugacy classes & character table

175 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, 1114268);