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C22×C13×#555 #15749046

order3328
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C26×C13 · Schur multiplier (H2) = C212×C4

Aliases

direct productC22×C13×#555

Subgroups

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

8710 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)(8,12)(9,10)(14,15)(18,19);(6,10)(8,11)(13,14,17,15)(16,19,20,18);(5,7,9,12)(6,11,10,8)(13,15,17,14)(16,19,20,18);(5,8,9,11)(6,12,10,7)(13,16,17,20)(14,18,15,19)

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, 55695);