C₂₉×#3552 #16817266

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

Aliases

direct product

C₂₉×#3552

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8499, C₂₉×#18694, C₂₉×#18695, …
maximal normal subgroup of	C₂₉×#8499, C₂₉×#18694, C₂₉×#18695, …
maximal quotient of	C₂₉×#34371, C₂₉×#34384, C₂₉×#34417, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2284);

C29×#3552 #16817266