C₁₉×#3140 #14560997

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#3140

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

400 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 608

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

Conjugacy classes & character table

608 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9439, C₁₉×#10022, C₁₉×#10024, …
maximal normal subgroup of	C₁₉×#9439, C₁₉×#10022, C₁₉×#10024, …
maximal quotient of	C₁₉×#20765, C₁₉×#21094, C₁₉×#21095, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1872);