C₁₉×#2984 #14560841

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#2984

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

364 conjugacy classes of subgroups; only the 272 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 272 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)(20,21,24,25,23,27,22,26)(28,29)(30,36)(31,34)(32,35)(33,38)(37,42)(39,41)(40,43);(20,22,23,24)(21,25,27,26)(28,30,32,38)(29,33,35,36)(31,39,40,37)(34,42,43,41);(20,22,23,24)(21,26,27,25)(28,31,32,40)(29,34,35,43)(30,37,38,39)(33,41,36,42);(21,27)(25,26)(29,35)(33,36)(34,43)(41,42)

Conjugacy classes & character table

950 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9164, C₁₉×#9166, C₁₉×#9244, …
maximal normal subgroup of	C₁₉×#9164, C₁₉×#9166, C₁₉×#9244, …
maximal quotient of	C₁₉×#20535, C₁₉×#20572, C₁₉×#20573, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1716);