C₂×C₂₉×#341 #16815451

order	3712
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×C₂₉×#341

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₉	D₄
commutator	C₄	C₂×C₄²×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
socle	C₂³×C₂₉	C₄⋊C₄
prime radical	C₂⁴×C₂₉	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(3,4)(5,6)(7,8,10,15,12,16,11,14)(9,17,18,13,20,21,19,22);(4,6)(7,9,11,19,12,20,10,18)(8,13,15,21,16,22,14,17)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7259, C₂₉×#7261, C₂₉×#7263, …
maximal normal subgroup of	C₂₉×#7259, C₂₉×#7261, C₂₉×#7263, …
maximal quotient of	C₂×C₂₉×#1277, C₂₉×#7872, C₂₉×#7874, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 469);

C2×C29×#341 #16815451