C₂₉×#2108 #16815822

order	3712
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₂₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₉×#2108

Subgroups

	subgroup	G/H
center	C₂×C₁₆×C₂₉	C₂²
commutator	C₂	C₂×C₄×C₈×C₂₉
Frattini, cosocle	C₂×C₈	C₂³×C₂₉
socle	C₂²×C₂₉	C₂²×C₈
prime radical	C₂³×C₂₉	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₂₉ ◁ G

184 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 65
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 65 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)(34,35,37,41,38,42,47,53,39,43,48,54,49,55,59,63)(36,40,45,51,46,52,58,62,44,50,56,60,57,61,64,65);(30,31,32,33)(34,36)(35,40)(37,45)(38,46)(39,44)(41,51)(42,52)(43,50)(47,58)(48,56)(49,57)(53,62)(54,60)(55,61)(59,64)(63,65);(36,44)(40,50)(45,56)(46,57)(51,60)(52,61)(58,64)(62,65)

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7469, C₂₉×#7470, C₂₉×#12026, …
maximal normal subgroup of	C₂₉×#7469, C₂₉×#7470, C₂₉×#12026, …
maximal quotient of	C₂₉×#11399, C₂₉×#11401, C₁₆×M₁₆×C₂₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 840);