C₁₉×#1378 #14559235

order	2432
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1378

Subgroups

	subgroup	G/H
center	C₈×C₁₉	C₂²⋊C₄
commutator	C₂²	C₄×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂²×C₁₉
socle	C₂×C₁₉	#336
prime radical	C₂³×C₁₉	C₂×C₈
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

132 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 84 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 — 2 generators on 51 points:

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

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉×#1378, C₁₉×#12597, C₁₉×#12609, …
maximal normal subgroup of	C₂×C₁₉×#1378, C₁₉×#12597, C₁₉×#12609, …
maximal quotient of	C₁₉×#7140, C₁₉×#7144, C₁₉×#7147, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 110);