C₁₉×#2015 #14559872

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2015

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

390 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 108 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 — 3 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)(22,23)(28,29,33,37)(30,38,41,42)(31,36,32,35)(34,40,43,39);(21,23)(24,25)(26,27)(28,30,33,41)(29,34,37,43)(31,40,32,39)(35,42,36,38);(25,27)(29,35)(31,32)(34,42)(36,37)(38,43)(39,40)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#2015, C₁₉×#23421, C₁₉×#23423, …
maximal normal subgroup of	C₂×C₁₉×#2015, C₁₉×#23421, C₁₉×#23423, …
maximal quotient of	C₁₉×#9955, C₁₉×#9956, C₁₉×#9958, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 747);