C₁₉×#11859 #18017818

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×#11859

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×D₈
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

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

normal subgroups only

This group has 314 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) = 1216

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)(38,48)(39,45)(40,55)(41,57)(42,47)(43,50)(44,53)(46,56)(49,65)(51,59)(52,62)(54,64)(58,63)(60,67)(61,66);(20,22)(21,25)(23,31)(24,30)(26,34)(27,28)(29,32)(33,35)(36,38,42,52)(37,43,47,61)(39,50,54,66)(40,49,53,67)(41,58,56,51)(44,62,55,48)(45,63,64,59)(46,65,57,60);(20,23,24,32)(21,26,27,35)(22,29,30,31)(25,33,28,34)(36,39,41,53,42,54,56,40)(37,44,46,45,47,55,57,64)(38,49,51,66,52,67,58,50)(43,59,60,48,61,63,65,62)

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, 4847);