C₂₉×#3417 #16817131

order	3712
nilpotency class	4
isoclinism	isoclinic class of #3415
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#3417

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₉	C₂²×D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₂₉
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ #41×C₂₉ ◁ C₂₉×#131 ◁ G

350 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 180 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 — 4 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)(30,31,36,41)(32,42,46,70)(33,38,47,61)(34,50,54,68)(35,55,52,40)(37,57,60,44)(39,64,66,53)(43,69,71,91)(45,74,56,65)(48,77,75,90)(49,80,76,63)(51,67,82,59)(58,83,84,72)(62,87,86,79)(73,92,81,88)(78,89,93,85);(30,32,36,46)(31,37,41,60)(33,43,47,71)(34,51,54,82)(35,56,52,45)(38,58,61,84)(39,65,66,74)(40,67,55,59)(42,68,70,50)(44,64,57,53)(48,78,75,93)(49,81,76,73)(62,88,86,92)(63,89,80,85)(69,90,91,77)(72,87,83,79);(30,33)(31,38)(32,43)(34,48)(35,49)(36,47)(37,58)(39,62)(40,63)(41,61)(42,69)(44,72)(45,73)(46,71)(50,77)(51,78)(52,76)(53,79)(54,75)(55,80)(56,81)(57,83)(59,85)(60,84)(64,87)(65,88)(66,86)(67,89)(68,90)(70,91)(74,92)(82,93);(33,47)(38,61)(43,71)(48,75)(49,76)(58,84)(62,86)(63,80)(69,91)(72,83)(73,81)(77,90)(78,93)(79,87)(85,89)(88,92)

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₉×#13670, C₂₉×#13672, C₂₉×#33855, …
maximal normal subgroup of	C₂₉×#13670, C₂₉×#13672, C₂₉×#33855, …
maximal quotient of	C₂₉×#33382, C₂₉×#33410, C₂₉×#33455, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2149);