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C13×#15347 #15701686

order3328
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C13 · Schur multiplier (H2) = C25

Aliases

direct productC13×#15347

Subgroups

subgroupG/H
center, socle, prime radicalC24×C13C24
commutator, Frattini, cosocleC24C24×C13
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

1318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 3328

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,21,20)(28,31)(29,33);(19,20)(23,25)(26,27,30,32)(28,29,31,33);(22,23)(24,25)(26,28,30,31)(27,29,32,33);(14,15)(16,17)(18,20,21,19)(26,29)(27,31)(28,32)(30,33)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 8335);