C₁₉×#1482 #14559339

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1482

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₄²	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₂²⋊C₄
prime radical	C₁₉×#121	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

212 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 92 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)(22,29)(23,27)(24,32)(25,28)(26,30)(31,34)(33,35)(36,37,39,42,40,43,46,49)(38,41,45,48,44,47,50,51);(20,22)(21,26)(23,30)(24,33)(25,31)(27,34)(28,35)(29,32)(36,38)(37,41)(39,45)(40,44)(42,48)(43,47)(46,50)(49,51);(20,23,25,24)(21,27,28,32)(22,30,31,33)(26,34,35,29)(38,44)(41,47)(45,50)(48,51)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8489, C₁₉×#8490, C₁₉×#8514, …
maximal normal subgroup of	C₁₉×#8489, C₁₉×#8490, C₁₉×#8514, …
maximal quotient of	C₁₉×#7656, C₁₉×#7657, C₁₉×#7658, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 214);