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C29×#1716 #16815430

order3712
nilpotency class3
isoclinismisoclinic class of #1714
automorphism?
homologyAbelianization (H1) = C23×C29 · Schur multiplier (H2) = C8

Aliases

direct productC29×#1716

Subgroups

subgroupG/H
center, socle, prime radicalC22×C29#127
commutator, Frattini, cosocleC42C23×C29
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C42×C29 ◁ G

176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 53
transitive degreeμt(G) = 3712

A minimal faithful permutation representation — 3 generators on 53 points:

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

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC29×#7534, C29×#12367, C2×C29×#1716, …
maximal normal subgroup ofC29×#7534, C29×#12367, C2×C29×#1716, …
maximal quotient ofC29×#8819, C29×#9826, C29×#9828, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 448);