C₂₉×#1423 #16815137

order	3712
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₉×#1423

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₉	D₁₆
commutator	C₁₆	C₂×C₄×C₂₉
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₉
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₂×C₈×C₂₉ ◁ C₂×C₁₆×C₂₉ ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 2 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)(30,31,32,33)(35,40)(36,41)(37,45)(38,48)(42,57)(43,60)(44,53)(46,62)(47,56)(49,61)(50,51)(52,58)(54,55)(59,65)(63,64);(34,35,41,51,37,42,54,60,48,58,62,65,61,63,47,53,39,44,56,64,49,59,46,52,38,43,55,57,45,50,36,40)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7537, C₂₉×#7538, C₂₉×#7545, …
maximal normal subgroup of	C₂₉×#7537, C₂₉×#7538, C₂₉×#7545, …
maximal quotient of	C₂₉×#7460, C₂₉×#7471, C₂₉×#7545, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 155);

C29×#1423 #16815137