C₂₉×#3543 #16817257

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

Aliases

direct product

C₂₉×#3543

Subgroups

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

1260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 5 generators on 45 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)(38,39)(40,42)(41,44)(43,45);(31,35)(32,36)(39,40)(43,44);(38,39,42,40)(41,43,45,44);(30,32,34,36)(31,33,35,37)(38,40,42,39)(41,44,45,43);(30,33)(31,36)(32,35)(34,37)(38,41)(39,43)(40,44)(42,45)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8497, C₂₉×#12767, C₂₉×#18682, …
maximal normal subgroup of	C₂₉×#8497, C₂₉×#12767, C₂₉×#18682, …
maximal quotient of	C₂₉×#34364, C₂₉×#34384, C₂₉×#34408, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2275);

C29×#3543 #16817257