C₁₉×#2162 #14560019

order	2432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#2162

Subgroups

	subgroup	G/H
center	C₄×C₈×C₁₉	C₂²
commutator	C₂	C₂²×C₁₆×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂²×C₈
prime radical	C₂³×C₁₉	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₁₉ ◁ G

160 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 120 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)(22,25)(23,24)(26,27)(28,29,30,33,31,34,36,39,32,35,37,40,38,41,42,43);(21,24)(25,27);(20,22,23,26)(21,25,24,27)

Conjugacy classes & character table

1520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₉×#7142, C₁₉×#7144, C₁₉×#7145, …
maximal normal subgroup of	C₁₉×#7142, C₁₉×#7144, C₁₉×#7145, …
maximal quotient of	C₁₉×#12590, C₄×C₁₉×C₂²⋊C₁₆, C₄×C₁₉×C₄⋊C₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 894);