C₂₉×#3542 #16817256

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

Aliases

direct product

C₂₉×#3542

Subgroups

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

1160 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)(30,31,34,32)(33,36,37,35)(39,42)(40,44);(31,32)(35,36)(39,42)(43,45);(38,39)(40,43)(41,42)(44,45);(30,32,34,31)(33,36,37,35)(38,40)(39,43)(41,44)(42,45);(30,33,34,37)(31,35,32,36)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#61609, C₂₉×#61611, C₂₉×#61614, …
maximal normal subgroup of	C₂₉×#61609, C₂₉×#61611, C₂₉×#61614, …
maximal quotient of	C₂₉×#34362, C₂₉×#34363, C₂₉×#34404, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2274);

C29×#3542 #16817256