C₁₉×#1535 #14559392

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1535

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
prime radical	C₁₉×#121	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

200 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 51
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,29,25,28,23,27)(22,30,31,35,32,26,33,34)(36,37)(38,44,46,51)(39,43)(40,42)(41,45,49,47)(48,50);(20,22)(21,26)(23,31)(24,33)(25,32)(27,34)(28,30)(29,35)(36,38)(37,41)(39,47)(40,46)(42,49)(43,51)(44,50)(45,48);(20,23,25,24)(21,27,28,29)(22,31,32,33)(26,34,30,35)(37,42)(41,49)(43,50)(44,51)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8489, C₁₉×#8490, C₁₉×#8500, …
maximal normal subgroup of	C₁₉×#8489, C₁₉×#8490, C₁₉×#8500, …
maximal quotient of	C₁₉×#7594, C₁₉×#7596, C₁₉×#7599, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 267);