C₂₉×#3586 #16817300

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3585
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂₉×#3586

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	C₂³×D₄
commutator, Frattini, cosocle	C₄	C₂⁵×C₂₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×#41×C₂₉ ◁ G

1412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 5 generators on 61 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)(32,40)(33,37)(34,46)(35,38)(36,42)(39,48)(41,54)(43,53)(44,51)(45,58)(47,50)(49,56)(52,57)(55,61)(59,60);(30,32,35,43)(31,36,38,50)(33,41,44,55)(34,47,48,42)(37,49,51,60)(39,53,46,40)(45,59,57,56)(52,61,58,54);(30,33)(31,37)(32,41)(34,45)(35,44)(36,49)(38,51)(39,52)(40,54)(42,56)(43,55)(46,58)(47,59)(48,57)(50,60)(53,61);(33,44)(37,51)(41,55)(45,57)(49,60)(52,58)(54,61)(56,59);(31,38)(36,50)(37,51)(39,46)(40,53)(49,60)(52,58)(54,61)

Conjugacy classes & character table

1189 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#23873, C₂₉×#23875, C₂₉×#23884, …
maximal normal subgroup of	C₂₉×#23873, C₂₉×#23875, C₂₉×#23884, …
maximal quotient of	C₂₉×#60088, C₂₉×#60089, C₂₉×#60109, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2318);

C29×#3586 #16817300