C₂₉×#3080 #16816794

order	3712
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#3080

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
prime radical	C₂×#41×C₂₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄²×C₂₉ ◁ G

384 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 200 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)(30,31,33,35)(32,36,37,34)(38,39,42,44)(40,48,50,53)(41,47,43,46)(45,51,52,49);(30,32,33,37)(31,34,35,36)(39,44)(45,52)(46,47)(48,53);(38,40)(39,45)(41,49)(42,50)(43,51)(44,52)(46,48)(47,53);(38,41,42,43)(39,46,44,47)(40,49,50,51)(45,48,52,53)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#9351, C₂₉×#9352, C₂₉×#24724, …
maximal normal subgroup of	C₂₉×#9351, C₂₉×#9352, C₂₉×#24724, …
maximal quotient of	C₂₉×#20649, C₂₉×#20875, C₂₉×#21034, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1812);