C₂₉×#1400 #16815114

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

Aliases

direct product

C₂₉×#1400

Subgroups

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

74 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)(30,31,32,37,33,38,41,49,34,39,42,50,43,51,54,59,35,36,40,46,44,47,52,56,45,48,53,57,55,58,60,61);(31,36)(32,40)(38,47)(39,48)(41,52)(42,53)(51,58)(54,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7336, C₂₉×#7337, C₂₉×#7364, …
maximal normal subgroup of	C₂₉×#7336, C₂₉×#7337, C₂₉×#7364, …
maximal quotient of	C₂₉×#7334, C₂₉×#7362, C₂₉×#7380, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 132);

C29×#1400 #16815114