C₂₉×#2570 #16816284

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

Aliases

direct product

C₂₉×#2570

Subgroups

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

380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 3712

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#26094, C₂₉×#26095, C₂₉×#26096, …
maximal normal subgroup of	C₂₉×#26094, C₂₉×#26095, C₂₉×#26096, …
maximal quotient of	C₂₉×#13909, C₂₉×#13955, C₂₉×#13981, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1302);

C29×#2570 #16816284