C₁₉×#23470 #18029429

order	4864
nilpotency class	3
isoclinism	isoclinic class of #23444
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#23470

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂⁴
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

1178 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 334 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) = 1216

A minimal faithful permutation representation — 4 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25)(22,26,27,24)(28,29)(30,34)(31,35)(32,36)(33,37)(38,48)(39,46)(40,47)(41,49)(42,50)(43,51)(44,52)(45,54)(53,58)(55,57)(56,59);(20,22,23,27)(21,24,25,26)(28,30)(29,34)(31,38)(32,39)(33,40)(35,48)(36,46)(37,47)(41,53)(42,54)(43,55)(44,56)(45,50)(49,58)(51,57)(52,59);(28,31,33,42)(29,35,37,50)(30,38,40,54)(32,43,44,41)(34,45,47,48)(36,51,52,49)(39,55,56,53)(46,58,59,57);(28,32,33,44)(29,36,37,52)(30,39,40,56)(31,41,42,43)(34,46,47,59)(35,49,50,51)(38,53,54,55)(45,57,48,58)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 16458);