C₁₉×#3080 #14560937

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#3080

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

384 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9351, C₁₉×#9352, C₁₉×#24724, …
maximal normal subgroup of	C₁₉×#9351, C₁₉×#9352, C₁₉×#24724, …
maximal quotient of	C₁₉×#20649, C₁₉×#20875, C₁₉×#21034, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1812);