C₂₉×#2273 #16815987

order	3712
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₂₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₉×#2273

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂⁴
commutator	C₂	C₂²×C₄²×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂⁵×C₂₉	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ G

912 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)(34,35,37,36)(38,39)(40,44)(41,42)(43,45);(30,31,32,33)(34,36,37,35)(39,42)(43,44);(38,39)(40,43)(41,42)(44,45);(38,40)(39,43)(41,45)(42,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8734, C₂₉×#9407, C₂₉×#9409, …
maximal normal subgroup of	C₂₉×#8734, C₂₉×#9407, C₂₉×#9409, …
maximal quotient of	C₂₉×#13749, C₂₉×#13775, C₂₉×#13778, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1005);

C29×#2273 #16815987