C₁₉×#3135 #14560992

order	2432
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#3135

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×D₄
prime radical	C₁₉×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

392 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 184 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)(22,25)(23,24)(26,27)(28,29)(30,39)(31,35)(32,37)(33,42)(34,38)(36,41)(40,43);(21,24)(25,27)(28,30,33,31,34,41,32,40)(29,35,37,39,38,43,42,36);(20,22,23,26)(21,25,24,27)(28,31,33,41,34,40,32,30)(29,36,37,35,38,39,42,43);(28,32,34,33)(29,37,38,42)(30,40,41,31)(35,39,43,36)

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9005, C₁₉×#9008, C₁₉×#10033, …
maximal normal subgroup of	C₁₉×#9005, C₁₉×#9008, C₁₉×#10033, …
maximal quotient of	C₁₉×#20762, C₁₉×#21086, C₁₉×#21199, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1867);