C₂₉×#2575 #16816289

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2575

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₉×#2575, C₂₉×#34849, C₂₉×#34866, …
maximal normal subgroup of	C₂×C₂₉×#2575, C₂₉×#34849, C₂₉×#34866, …
maximal quotient of	C₂₉×#13917, C₂₉×#13950, C₂₉×#13983, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1307);

C29×#2575 #16816289