C₁₉×#11865 #18017824

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11858
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#11865

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

300 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 67
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28,30,25)(23,26)(24,27)(29,34,31,33)(32,35)(36,37,41,47,43,48,42,57)(38,49,52,59,53,63,58,64)(39,46,40,56,55,65,54,45)(44,50,60,66,62,67,61,51);(20,22)(21,25)(23,31)(24,30)(26,34)(27,28)(29,32)(33,35)(36,38,43,53)(37,44,48,62)(39,51,55,66)(40,50,54,67)(41,52,42,58)(45,63,56,49)(46,64,65,59)(47,60,57,61);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(36,39,42,54,43,55,41,40)(37,45,47,46,48,56,57,65)(38,50,52,66,53,67,58,51)(44,59,61,49,62,64,60,63)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4853);