C₂₉×#2170 #16815884

order	3712
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₉×#2170

Subgroups

	subgroup	G/H
center	C₁₆×C₂₉	D₄
commutator	C₄	C₂²×C₈×C₂₉
Frattini, cosocle	C₂×C₈	C₂³×C₂₉
socle	C₂×C₂₉	C₈×D₄
prime radical	C₂₉×#135	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₂₉ ◁ C₂×C₁₆×C₂₉ ◁ G

146 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 92 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)(30,31,35,39,34,40,49,57,36,41,51,58,50,38,54,56)(32,42,44,47,45,53,59,48,46,55,60,61,43,37,52,33);(30,32)(31,37)(33,39)(34,45)(35,44)(36,46)(38,55)(40,42)(41,53)(43,50)(47,57)(48,58)(49,59)(51,60)(52,54)(56,61);(30,33,35,42,34,47,49,53,36,48,51,55,50,61,54,37)(31,32,39,44,40,45,57,59,41,46,58,60,38,43,56,52)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7381, C₂₉×#7382, C₂₉×#12046, …
maximal normal subgroup of	C₂₉×#7381, C₂₉×#7382, C₂₉×#12046, …
maximal quotient of	C₁₆×D₈×C₂₉, C₂₉×#12039, C₁₆×SD₁₆×C₂₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 902);