C₁₉×#12164 #18018123

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12164

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#424 ◁ G

374 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 74 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 — 3 generators on 59 points:

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

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5152);