C₂₉×#1440 #16815154

order	3712
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₉×#1440

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₂₉	C₂³
commutator	C₂³	C₂²×C₄×C₂₉
Frattini, cosocle	C₂⁴	C₂³×C₂₉
prime radical	C₂⁵×C₂₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

736 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 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)(38,39,40,41)(42,43,45,44);(31,33)(35,37)(43,44);(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,44,45,43)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7324, C₂₉×#8535, C₂×C₂₉×#1440, …
maximal normal subgroup of	C₂₉×#7324, C₂₉×#8535, C₂×C₂₉×#1440, …
maximal quotient of	C₂₉×#7555, C₂₉×#7556, C₂₉×#11147, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 172);