C₂₉×#2968 #16816682

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₉×#2968

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂₉×#121	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

372 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 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)(32,35)(33,34)(36,37)(38,39,41,44,42,45,48,51)(40,43,47,50,46,49,52,53);(31,34)(35,37);(38,40,41,47,42,46,48,52)(39,43,44,50,45,49,51,53);(30,32,33,36)(31,35,34,37)(40,46)(43,49)(47,52)(50,53)

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#9265, C₂₉×#9266, C₂₉×#9431, …
maximal normal subgroup of	C₂₉×#9265, C₂₉×#9266, C₂₉×#9431, …
maximal quotient of	C₂₉×#20478, C₂₉×#20481, C₂₉×#20492, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1700);

C29×#2968 #16816682