C₁₉×#11490 #18017449

order	4864
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#11490

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	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×C₈×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

364 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 138 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)(28,29,33,39,35,38,47,55,34,40,46,56,32,48,31,37)(30,41,44,51,43,36,50,52,45,54,58,59,49,53,42,57);(21,24)(22,26)(28,30)(29,36)(31,42)(32,49)(33,44)(34,45)(35,43)(37,51)(38,54)(39,52)(40,53)(41,48)(46,58)(47,50)(55,59)(56,57);(28,31,32,46,34,47,35,33)(29,37,48,56,40,55,38,39)(30,42,49,58,45,50,43,44)(36,51,41,57,53,59,54,52)

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4478);