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C22×C13×#540 #15749016

order3328
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C26×C13 · Schur multiplier (H2) = C213

Aliases

direct productC22×C13×#540

Subgroups

subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC22C26×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

8838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 1664

A minimal faithful permutation representation — 6 generators on 33 points:

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

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 55665);