C₁₉×#2115 #14559972

order	2432
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2115

Subgroups

	subgroup	G/H
center	C₈×C₁₉	C₂²⋊C₄
commutator	C₂²	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂×C₁₉	C₂×C₂²⋊C₈
prime radical	C₂×#41×C₁₉	C₄
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

220 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 116 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,28,24,29,35,43,25,27,36,40,37,41,48,50)(22,30,32,42,33,44,46,51,31,26,34,38,45,39,47,49);(20,22)(21,26)(23,34)(24,33)(25,31)(27,30)(28,42)(29,39)(32,36)(35,47)(37,45)(38,40)(41,44)(43,51)(46,48)(49,50);(22,31)(26,30)(32,34)(33,45)(38,42)(39,44)(46,47)(49,51)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7207, C₁₉×#7208, C₁₉×#11483, …
maximal normal subgroup of	C₁₉×#7207, C₁₉×#7208, C₁₉×#11483, …
maximal quotient of	C₁₉×#11419, C₁₉×#11441, C₁₉×#11461, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 847);