C₂₉×#2517 #16816231

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₉×#2517

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂⁴×C₂₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(35,37)(38,39,42,40)(41,44,45,43)(46,47,50,49)(48,52,53,51);(39,40)(43,44)(48,53)(51,52);(30,31)(32,35)(33,34)(36,37)(38,40,42,39)(41,44,45,43)(46,48)(47,51)(49,52)(50,53);(30,32,33,36)(31,35,34,37)(38,41)(39,43)(40,44)(42,45)(46,49,50,47)(48,52,53,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#12135, C₂₉×#12229, C₂×C₂₉×#2517, …
maximal normal subgroup of	C₂₉×#12135, C₂₉×#12229, C₂×C₂₉×#2517, …
maximal quotient of	C₂₉×#13888, C₂₉×#14009, C₂₉×#14061, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1249);

C29×#2517 #16816231