C₁₉×#8788 #18014747

order	4864
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#8788

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
socle, prime radical	C₂³×C₁₉	C₂×C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ C₄³×C₁₉ ◁ G

322 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 59
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 59 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)(30,38)(31,34)(32,42)(33,37)(35,40)(36,39)(41,43)(44,45,47,50,48,51,54,57)(46,49,53,56,52,55,58,59);(21,24)(25,27)(28,30,39,41,33,40,32,31)(29,34,42,35,37,43,36,38)(44,46)(45,49)(47,53)(48,52)(50,56)(51,55)(54,58)(57,59);(20,22,23,26)(21,25,24,27)(28,31,32,40,33,41,39,30)(29,35,36,34,37,38,42,43)(46,52)(49,55)(53,58)(56,59)

Conjugacy classes & character table

1216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1776);