C₂₉×#3545 #16817259

order	3712
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₉×#3545

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

1060 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 5 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)(38,39)(40,46)(41,43)(42,49)(44,47)(45,50)(48,51)(52,53);(31,34)(35,37)(39,41)(40,47)(45,49)(48,53);(30,31,33,34)(32,35,36,37)(38,40)(39,44)(41,46)(42,48)(43,47)(45,51)(49,52)(50,53);(30,32)(31,35)(33,36)(34,37)(38,41,43,39)(40,46,47,44)(42,49,50,45)(48,52,53,51);(38,42)(39,45)(40,48)(41,49)(43,50)(44,51)(46,52)(47,53)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8528, C₂₉×#12768, C₂₉×#12781, …
maximal normal subgroup of	C₂₉×#8528, C₂₉×#12768, C₂₉×#12781, …
maximal quotient of	C₂₉×#34366, C₂₉×#34390, C₂₉×#34408, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2277);

C29×#3545 #16817259