C₁₉×#10382 #18016341

order	4864
nilpotency class	3
isoclinism	isoclinic class of #10382
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#10382

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#393
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

446 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 43
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 43 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)(30,36,38,42)(31,34)(32,35)(33,39,37,40)(41,43);(22,27)(24,25)(28,29)(30,37,38,33)(31,34)(32,35)(36,39,42,40)(41,43);(21,24)(22,27)(25,26)(28,30)(29,33)(31,40)(32,38)(34,42)(35,37)(36,43)(39,41)

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, 3370);