C₂₉×#2222 #16815936

order	3712
nilpotency class	4
isoclinism	isoclinic class of #2221
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2222

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	#466
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₉
prime radical	#41×C₂₉	D₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₂₉×#131 ◁ G

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

normal subgroups only

This group has 140 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) = 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)(32,44,50,72)(33,51,54,68)(34,55,57,66)(35,42,36,41)(38,59,63,47)(39,58,65,53)(40,56,67,45)(46,75,78,92)(48,71,49,70)(52,83,84,64)(60,87,88,93)(61,79,62,73)(69,80,91,77)(74,82,85,90)(76,81,86,89);(30,32,45,73,36,49,57,59,37,50,56,79,35,48,34,47)(31,38,55,71,42,62,67,72,43,63,66,70,41,61,40,44)(33,46,74,93,53,77,84,86,54,78,85,87,58,80,52,76)(39,60,82,75,51,81,83,91,65,88,90,92,68,89,64,69);(30,33)(31,39)(32,46)(34,52)(35,58)(36,53)(37,54)(38,60)(40,64)(41,68)(42,51)(43,65)(44,69)(45,74)(47,76)(48,80)(49,77)(50,78)(55,82)(56,85)(57,84)(59,86)(61,89)(62,81)(63,88)(66,90)(67,83)(70,92)(71,75)(72,91)(73,93)(79,87)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#13671, C₂₉×#13672, C₂₉×#13701, …
maximal normal subgroup of	C₂₉×#13671, C₂₉×#13672, C₂₉×#13701, …
maximal quotient of	C₂₉×#12431, C₂₉×#12434, C₂₉×#12440, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 954);