C₂₉×#3544 #16817258

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

Aliases

direct product

C₂₉×#3544

Subgroups

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

1004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1856

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8498, C₂₉×#12782, C₂₉×#18684, …
maximal normal subgroup of	C₂₉×#8498, C₂₉×#12782, C₂₉×#18684, …
maximal quotient of	C₂₉×#34365, C₂₉×#34384, C₂₉×#34409, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2276);

C29×#3544 #16817258