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C2×C32×C5×C13×C29 #46800239

order33930
nilpotency class1
automorphism?
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC2×C32×C5×C13×C29

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 55
transitive degreeμt(G) = 33930

A minimal faithful permutation representation — 2 generators on 55 points:

(1,2)(3,4,5)(9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55);(6,7,8)

Conjugacy classes & character table

33930 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 25);