C₂₉×#2982 #16816696

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×#2982

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	C₂³×C₂₉	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

396 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)(30,31,32,34,33,35,36,37)(38,39)(40,46)(41,44)(42,45)(43,48)(47,52)(49,51)(50,53);(38,40,42,48)(39,43,45,46)(41,49,50,47)(44,52,53,51);(38,41,42,50)(39,44,45,53)(40,47,48,49)(43,51,46,52);(39,45)(43,46)(44,53)(51,52)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8836, C₂₉×#8958, C₂₉×#8960, …
maximal normal subgroup of	C₂₉×#8836, C₂₉×#8958, C₂₉×#8960, …
maximal quotient of	C₂₉×#20533, C₂₉×#20569, C₂₉×#21818, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1714);

C29×#2982 #16816696