C₂₉×#2110 #16815824

order	3712
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2110

Subgroups

	subgroup	G/H
center	C₈×C₂₉	C₄²
commutator	C₄	C₂×C₄²×C₂₉
Frattini, cosocle	C₂×C₈	C₂³×C₂₉
socle	C₂×C₂₉	C₂×#97
prime radical	C₂³×C₂₉	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₈×C₂₉ ◁ G

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(30,31,33,37,34,39,45,53,35,38,46,52,47,54,60,61)(32,40,42,56,43,49,58,51,41,55,44,59,57,36,48,50);(30,32)(31,36,38,49)(33,44)(34,43)(35,41)(37,51,52,50)(39,40,54,55)(42,46)(45,48)(47,57)(53,59,61,56)(58,60);(32,41)(36,49)(40,55)(42,44)(43,57)(48,58)(50,51)(56,59)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#11912, C₂₉×#11913, C₂₉×#11914, …
maximal normal subgroup of	C₂₉×#11912, C₂₉×#11913, C₂₉×#11914, …
maximal quotient of	C₂₉×#11405, C₂₉×#11406, C₂₉×#11413, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 842);

C29×#2110 #16815824