C₂₉×#2214 #16815928

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2214

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	#459
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	C₂₉×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₄×C₈×C₂₉ ◁ G

150 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 61
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 3 generators on 61 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)(30,31,37,43)(32,41,46,52)(33,47,49,60)(34,42,36,40)(35,38,45,53)(39,54,56,44)(48,61,51,57)(50,58,59,55);(30,32,36,45,37,46,34,35)(31,38,42,52,43,53,40,41)(33,44,51,59,49,54,48,50)(39,47,58,61,56,60,55,57);(30,33)(31,39)(32,44)(34,48)(35,50)(36,51)(37,49)(38,47)(40,55)(41,57)(42,58)(43,56)(45,59)(46,54)(52,61)(53,60)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#12312, C₂₉×#12313, C₂₉×#12315, …
maximal normal subgroup of	C₂₉×#12312, C₂₉×#12313, C₂₉×#12315, …
maximal quotient of	C₂₉×#12422, C₂₉×#12423, C₂₉×#12426, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 946);