C₁₉×#7393 #18013352

order	4864
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#7393

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₁₆×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
socle, prime radical	C₂²×C₁₉	C₂²⋊C₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

110 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 62 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) = 4864

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)(21,24)(22,26)(25,27)(28,29,31,37,33,38,44,52,34,35,42,47,46,48,55,57,32,36,43,49,45,50,56,58,30,39,40,51,41,53,54,59);(20,21,23,25)(22,27,26,24)(28,30,32,34)(29,35,36,39)(31,42,43,40)(33,41,45,46)(37,51,49,47)(38,48,50,53)(44,55,56,54)(52,59,58,57)

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, 381);