C₁₉×#1735 #14559592

order	2432
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#1735

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	D₄
commutator	C₄	C₂×C₄²×C₁₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₉
socle	C₂³×C₁₉	C₂×D₄
prime radical	C₂⁴×C₁₉	D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

424 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 232 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 — 3 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)(22,23)(24,25,26,27)(28,29)(30,38)(31,35)(32,36)(33,37)(34,39)(40,43)(41,42);(21,23)(28,30,32,40,33,41,31,39)(29,34,35,42,37,43,36,38);(28,31,33,32)(29,35,37,36)(30,39,41,40)(34,42,43,38)

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#7260, C₁₉×#7262, C₁₉×#10706, …
maximal normal subgroup of	C₁₉×#7260, C₁₉×#7262, C₁₉×#10706, …
maximal quotient of	C₁₉×#7872, C₁₉×#7875, C₁₉×#7878, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 467);