C₁₉×#2980 #14560837

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×#2980

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	C₁₉×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

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

normal subgroups only

This group has 394 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) = 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)(22,26)(23,25)(24,27)(28,29,31,35,32,36,39,43)(30,33,38,40,37,34,41,42);(20,22)(21,24)(23,27)(25,26)(28,30)(29,33)(31,38)(32,37)(34,36)(35,40)(39,41)(42,43);(22,27)(24,26)(28,30)(29,34)(31,38)(32,37)(33,36)(35,42)(39,41)(40,43);(21,25)(24,26)(30,37)(33,34)(38,41)(40,42)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#8918, C₁₉×#9005, C₁₉×#9007, …
maximal normal subgroup of	C₁₉×#8918, C₁₉×#9005, C₁₉×#9007, …
maximal quotient of	C₁₉×#20532, C₁₉×#20539, C₁₉×#20563, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1712);