C₂×C₂₉×#449 #16816714

order	3712
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₂₉×#449

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₉ ◁ C₂³×C₄×C₂₉ ◁ G

812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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);(3,4)(5,6)(8,12)(9,10)(13,14);(7,8)(9,12)(10,14)(11,13);(4,6)(7,9,11,10)(8,12,13,14)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#9241, C₄×C₂₉×#449, C₂₉×#21456, …
maximal normal subgroup of	C₂₉×#9241, C₄×C₂₉×#449, C₂₉×#21456, …
maximal quotient of	C₂×C₂₉×#1597, C₂×C₂₉×#1609, C₂×C₂₉×#1600, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1732);

C2×C29×#449 #16816714