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C13×#13817 #15700156

order3328
nilpotency class2
automorphism?
homologyAbelianization (H1) = C22×C42×C13 · Schur multiplier (H2) = C25×C4

Aliases

direct productC13×#13817

Subgroups

subgroupG/H
center, socle, prime radicalC24×C13C24
commutatorC22C22×C42×C13
Frattini, cosocleC24C24×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

1970 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)(14,15)(16,17)(18,19)(20,21)(22,23,25,24)(27,30)(31,33);(15,17)(18,19,20,21);(22,23,25,24)(26,27)(28,31)(29,30)(32,33);(14,15)(16,17)(18,19)(20,21)(22,24,25,23)(26,28,29,32)(27,31,30,33)

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6805);