C₁₉×#20691 #18026650

order	4864
nilpotency class	3
isoclinism	isoclinic class of #17367
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#20691

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×Q₈×C₁₉ ◁ G

1266 conjugacy classes of subgroups; only the 446 normal subgroups are shown.

normal subgroups only

This group has 1266 conjugacy classes of subgroups — too many to draw. Only its 446 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)(22,25)(23,24)(26,27)(28,29)(30,34)(31,41,43,35)(32,36)(33,37)(38,52,54,46)(39,47)(40,48)(42,55,57,49)(44,50)(45,51)(53,59,56,58);(21,24)(25,27)(28,30,33,40)(29,34,37,48)(31,38,43,54)(32,44,45,39)(35,46,41,52)(36,50,51,47)(42,56,57,53)(49,59,55,58);(20,22,23,26)(21,25,24,27)(28,31)(29,35)(30,38)(32,42)(33,43)(34,46)(36,49)(37,41)(39,53)(40,54)(44,56)(45,57)(47,58)(48,52)(50,59)(51,55);(28,32,33,45)(29,36,37,51)(30,39,40,44)(31,42,43,57)(34,47,48,50)(35,49,41,55)(38,53,54,56)(46,58,52,59)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 13679);