C₂₉×#2195 #16815909

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2192
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#2195

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	#447
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	C₂₉×#578	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₂₉×#131 ◁ G

206 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 93
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 93 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)(32,44,48,72)(33,49,52,69)(34,53,57,67)(35,42,36,41)(38,60,63,46)(39,58,65,51)(40,55,68,56)(45,73,77,90)(47,78,59,66)(50,81,84,64)(54,70,85,62)(61,82,89,93)(71,76,92,75)(74,79,87,88)(80,86,91,83);(30,32)(31,38)(33,45)(34,54)(35,47)(36,59)(37,48)(39,61)(40,66)(41,62)(42,70)(43,63)(44,53)(46,56)(49,79)(50,82)(51,75)(52,77)(55,60)(57,85)(58,76)(64,90)(65,89)(67,72)(68,78)(69,88)(71,80)(73,81)(74,83)(84,93)(86,87)(91,92);(30,33,37,52)(31,39,43,65)(32,45,48,77)(34,50,57,84)(35,58,36,51)(38,61,63,89)(40,64,68,81)(41,69,42,49)(44,71,72,92)(46,74,60,87)(47,76,59,75)(53,80,67,91)(54,82,85,93)(55,86,56,83)(62,88,70,79)(66,90,78,73)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₉×#2195, C₂₉×#33538, C₂₉×#33540, …
maximal normal subgroup of	C₂×C₂₉×#2195, C₂₉×#33538, C₂₉×#33540, …
maximal quotient of	C₂₉×#12112, C₂₉×#12113, C₂₉×#12168, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 927);