C₂₉×#3539 #16817253

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

Aliases

direct product

C₂₉×#3539

Subgroups

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

1050 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)(40,43)(41,46)(42,47)(44,48)(45,50)(49,51)(52,53);(31,34)(35,37)(39,40)(41,48)(45,47)(49,53);(30,31)(32,35)(33,34)(36,37)(38,40,43,39)(41,46,48,44)(42,47,50,45)(49,52,53,51);(30,32)(31,35)(33,36)(34,37)(38,41)(39,44)(40,46)(42,49)(43,48)(45,51)(47,52)(50,53);(38,42,43,50)(39,45,40,47)(41,49,48,53)(44,51,46,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#61626, C₂₉×#61628, C₂₉×#61635, …
maximal normal subgroup of	C₂₉×#61626, C₂₉×#61628, C₂₉×#61635, …
maximal quotient of	C₂₉×#34361, C₂₉×#34391, C₂₉×#34410, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2271);

C29×#3539 #16817253