C₂₉×#2988 #16816702

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×#2988

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	C₂×#41×C₂₉	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

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)(31,34)(32,36)(38,39,40,42,41,43,44,45);(30,31)(32,35)(33,34)(36,37);(31,34)(35,37);(30,32,33,36)(31,35,34,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8839, C₂₉×#8840, C₂₉×#8953, …
maximal normal subgroup of	C₂₉×#8839, C₂₉×#8840, C₂₉×#8953, …
maximal quotient of	C₂₉×#20543, C₂₉×#20555, C₂₉×#20569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1720);

C29×#2988 #16816702