C₂×C₂₉×#550 #16817181

order	3712
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₉ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂×C₂₉×#550

Subgroups

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

1736 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 5 generators on 43 points:

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

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#8361, C₂₉×#8384, C₂₉×#8385, …
maximal normal subgroup of	C₂₉×#8361, C₂₉×#8384, C₂₉×#8385, …
maximal quotient of	C₂×C₂₉×#2341, C₂×Q₈×C₄⋊C₄×C₂₉, C₂×C₂₉×#2354, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2199);

C2×C29×#550 #16817181