C₂₉×#1422 #16815136

order	3712
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂₉×#1422

Subgroups

	subgroup	G/H
center	C₁₆×C₂₉	D₄
commutator	C₄	C₂×C₁₆×C₂₉
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₉
socle	C₂×C₂₉	C₄⋊C₁₆
prime radical	C₂²×C₂₉	M₃₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₂₉ ◁ C₂×C₁₆×C₂₉ ◁ G

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 2 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)(30,31,34,40,35,41,49,56,36,39,50,54,46,55,59,61,37,42,51,57,44,38,52,53,33,47,48,60,32,43,45,58);(30,32,33,44,37,46,36,35)(31,38,39,43,42,41,47,55)(34,45,48,52,51,59,50,49)(40,53,54,58,57,56,60,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7381, C₂₉×#7382, C₂₉×#7447, …
maximal normal subgroup of	C₂₉×#7381, C₂₉×#7382, C₂₉×#7447, …
maximal quotient of	C₂₉×#7455, C₂₉×#7458, C₂₉×#7467, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 154);

C29×#1422 #16815136