C₁₉×#11491 #18017450

order	4864
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#11491

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₂²⋊C₈
prime radical	C₁₉×#532	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

356 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 2432

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)(28,29,33,39,35,38,48,37,34,40,47,56,32,49,31,46)(30,41,44,57,43,36,51,53,45,55,59,52,50,54,42,58);(21,24)(22,26)(28,30)(29,36)(31,42)(32,50)(33,44)(34,45)(35,43)(37,52)(38,55)(39,53)(40,54)(41,49)(46,57)(47,59)(48,51)(56,58);(28,31,32,47,34,48,35,33)(29,37,49,39,40,46,38,56)(30,42,50,59,45,51,43,44)(36,52,41,53,54,57,55,58)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4479);