C₂₉×#2972 #16816686

order	3712
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₂₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₉×#2972

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₉	C₂⁴
commutator	C₂	C₂³×C₈×C₂₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
socle	C₂²×C₂₉	C₂³×C₄
prime radical	C₂²×D₄×C₂₉	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 928

A minimal faithful permutation representation — 4 generators on 45 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)(32,36)(33,35)(34,37)(38,39,40,42,41,43,44,45);(30,32)(31,34)(33,37)(35,36);(32,37)(34,36);(31,35)(34,36)

Conjugacy classes & character table

1972 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8835, C₂₉×#8851, C₂₉×#8957, …
maximal normal subgroup of	C₂₉×#8835, C₂₉×#8851, C₂₉×#8957, …
maximal quotient of	C₂₉×#20523, C₂₉×#20533, C₂₉×#20555, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1704);

C29×#2972 #16816686