C₁₉×#2123 #14559980

order	2432
nilpotency class	4
isoclinism	isoclinic class of #2121
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#2123

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#99
commutator	C₂³	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×D₄	C₂³×C₁₉
prime radical	C₂×#41×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

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

normal subgroups only

This group has 234 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 — 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)(22,30)(23,27)(24,37,38,28)(25,29)(26,32,40,47)(31,44)(33,45)(34,48)(35,50,51,42)(36,43)(39,46,41,49);(20,22,25,33)(21,26,29,40)(23,34,36,31)(24,32,38,47)(27,41,43,39)(28,30,37,45)(35,49,51,46)(42,48,50,44);(20,23,25,36)(21,27,29,43)(22,31,33,34)(24,35,38,51)(26,39,40,41)(28,42,37,50)(30,44,45,48)(32,46,47,49)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#12716, C₁₉×#12717, C₁₉×#12723, …
maximal normal subgroup of	C₁₉×#12716, C₁₉×#12717, C₁₉×#12723, …
maximal quotient of	C₁₉×#11428, C₁₉×#11454, C₁₉×#11474, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 855);