C₂×C₁₉×#486 #14560985

order	2432
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂×C₁₉×#486

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

528 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9057, C₁₉×#9062, C₁₉×#9735, …
maximal normal subgroup of	C₁₉×#9057, C₁₉×#9062, C₁₉×#9735, …
maximal quotient of	C₂×C₁₉×#1834, C₂×C₁₉×#1934, C₂×C₁₉×#1957, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1860);