C₁₉×#2178 #14560035

order	2432
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2178

Subgroups

	subgroup	G/H
center	C₈×C₁₉	D₈
commutator	C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂×C₁₉	C₄×D₈
prime radical	C₁₉×#508	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂×C₈×C₁₉ ◁ C₄×C₈×C₁₉ ◁ G

146 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 76 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)(20,21,25,29,26,31,41,30)(22,32,34,43,36,49,35,51)(23,28,37,46,38,47,24,39)(27,42,44,50,45,40,48,33);(20,22)(21,27)(23,33)(24,40)(25,34)(26,36)(28,43)(29,44)(30,48)(31,45)(32,39)(35,41)(37,42)(38,50)(46,49)(47,51);(20,23,25,37,26,38,41,24)(21,28,29,46,31,47,30,39)(22,33,34,42,36,50,35,40)(27,43,44,49,45,51,48,32)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7387, C₁₉×#7388, C₁₉×#12046, …
maximal normal subgroup of	C₁₉×#7387, C₁₉×#7388, C₁₉×#12046, …
maximal quotient of	C₈×C₁₉×D₁₆, C₈×C₁₉×SD₃₂, C₈×C₁₉×Q₃₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 910);