C₁₉×#7150 #18013109

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

Aliases

direct product

C₁₉×#7150

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂²⋊C₄
commutator	C₂×C₄	C₄×C₈×C₁₉
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₉
socle	C₂²×C₁₉	#336
prime radical	C₂³×C₁₉	C₂²⋊C₈
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

254 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 106 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 — 2 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)(22,24)(23,26)(25,27)(28,29,31,35,32,37,42,49,33,36,43,48,44,50,55,58)(30,38,40,51,41,52,54,59,39,34,45,46,53,47,56,57);(21,24,26,25)(28,30)(29,34,36,38)(31,40)(32,41)(33,39)(35,46,48,51)(37,47,50,52)(42,54)(43,45)(44,53)(49,57,58,59)(55,56)

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, 138);