C₂₉×#1380 #16815094

order	3712
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₄²×C₂₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₉×#1380

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₉	D₈
commutator	C₈	C₄²×C₂₉
Frattini, cosocle	C₂²×C₈	C₂²×C₂₉
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 3712

A minimal faithful permutation representation — 2 generators on 53 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)(34,35,36,37)(39,44)(40,48)(41,50)(42,49)(45,46)(47,53)(51,52);(31,33)(38,39,41,45,42,46,40,44,43,47,48,52,49,51,50,53)

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#7418, C₂₉×#7419, C₂×C₂₉×#1380, …
maximal normal subgroup of	C₂₉×#7418, C₂₉×#7419, C₂×C₂₉×#1380, …
maximal quotient of	C₂₉×#7154, C₂₉×#7171, C₂₉×#7217, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 112);

C29×#1380 #16815094