C₂₉×#2561 #16816275

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₉×#2561

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂⁵×C₂₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

672 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 928

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9407, C₂₉×#9411, C₂₉×#9942, …
maximal normal subgroup of	C₂₉×#9407, C₂₉×#9411, C₂₉×#9942, …
maximal quotient of	C₂₉×#13903, C₂₉×#13966, C₂₉×#13971, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1293);

C29×#2561 #16816275