C₂₉×#1454 #16815168

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₂₉×#1454

Subgroups

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

178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 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)(30,31,33,37,34,36,40,43)(32,35,39,41,38,42,44,45)(46,47)(48,51)(49,53)(50,52)(54,58)(55,57)(56,59)(60,61);(30,32)(31,35)(33,39)(34,38)(36,42)(37,41)(40,44)(43,45)(46,48,49,54,50,55,56,60)(47,51,53,58,52,57,59,61);(31,36)(32,38)(37,43)(39,44)(47,52)(51,57)(53,59)(58,61)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₂₉×#1454, C₂₉×#17324, C₂₉×#17326, …
maximal normal subgroup of	C₂×C₂₉×#1454, C₂₉×#17324, C₂₉×#17326, …
maximal quotient of	C₂₉×#7845, C₂₉×#7851, C₂₉×#8135, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 186);

C29×#1454 #16815168