C₂₉×#2644 #16816358

order	3712
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2644

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

420 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 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)(31,34)(35,36)(38,39)(40,43)(41,44)(42,45)(46,47,50,52)(48,53,49,51);(30,31,33,34)(32,35,37,36)(38,40)(39,41)(42,44)(43,45)(46,48,50,49)(47,51,52,53);(30,31)(32,36)(33,34)(35,37)(38,40)(39,43)(41,45)(42,44)(46,47)(48,51)(49,53)(50,52);(30,32,33,37)(31,35,34,36)(38,41,42,43)(39,44,45,40)(46,49,50,48)(47,51,52,53)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#29436, C₂₉×#29437, C₂₉×#29442, …
maximal normal subgroup of	C₂₉×#29436, C₂₉×#29437, C₂₉×#29442, …
maximal quotient of	C₂₉×#14260, C₂₉×#14266, C₂₉×#14331, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1376);