Finite Group Databasebeta

← Prev (#15710220) Next (#15710222) →

C13×#23882 #15710221

order3328
nilpotency class3
isoclinismisoclinic class of #23882
automorphism?
homologyAbelianization (H1) = C24×C13 · Schur multiplier (H2) = C27

Aliases

direct productC13×#23882

Subgroups

subgroupG/H
center, socleC2×C13#2403
commutator, Frattini, cosocleC22×C4C24×C13
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G

1866 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 208

A minimal faithful permutation representation — 4 generators on 29 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24)(17,22)(18,21)(19,23)(20,25)(26,29)(27,28);(14,16)(15,20)(17,27)(18,25)(19,26)(21,29)(22,24)(23,28);(15,21)(17,18)(20,24)(22,23)(25,27)(28,29);(15,22)(17,18)(20,24)(21,23)(25,27)(28,29)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 16870);