C₁₉×#2987 #14560844

order	2432
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2987

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂³×C₄
prime radical	C₂³×C₁₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

314 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 248 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 — 4 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)(22,28)(23,26)(24,27)(25,30)(29,34)(31,33)(32,35)(36,37,39,43,40,42,46,49)(38,41,45,48,44,47,50,51);(20,22,24,30)(21,25,27,28)(23,31,32,29)(26,34,35,33)(36,38)(37,41)(39,45)(40,44)(42,47)(43,48)(46,50)(49,51);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(37,42)(38,44)(43,49)(45,50);(21,27)(25,28)(26,35)(33,34)(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×#8919, C₁₉×#9006, C₁₉×#9008, …
maximal normal subgroup of	C₁₉×#8919, C₁₉×#9006, C₁₉×#9008, …
maximal quotient of	C₁₉×#20539, C₁₉×#20542, C₁₉×#20576, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1719);