C₂₉×#2405 #16816119

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#2405

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂³×D₄×C₂₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

1116 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 928

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#9496, C₂₉×#9498, C₂₉×#9499, …
maximal normal subgroup of	C₂₉×#9496, C₂₉×#9498, C₂₉×#9499, …
maximal quotient of	C₂₉×#13867, C₂₉×#13869, C₂₉×#13968, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1137);

C29×#2405 #16816119