Finite Group Databasebeta

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C29×#3109 #16816823

order3712
nilpotency class3
isoclinismisoclinic class of #3003
automorphism?
homologyAbelianization (H1) = C24×C29 · Schur multiplier (H2) = C25

Aliases

direct productC29×#3109

Subgroups

subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 928

A minimal faithful permutation representation — 4 generators on 45 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)(30,31)(32,35)(33,34)(36,37)(38,39)(40,45)(41,43)(42,44);(31,34)(35,37)(39,43)(44,45);(39,44)(40,42)(43,45);(30,32,33,36)(31,35,34,37)(38,40,41,42)(39,45,43,44)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC29×#9163, C29×#9325, C29×#9329, …
maximal normal subgroup ofC29×#9163, C29×#9325, C29×#9329, …
maximal quotient ofC29×#20738, C29×#21122, C29×#21365, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1841);