C₁₉×#13675 #18019634

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13673
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13675

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2196
commutator, Frattini, cosocle	#127	C₂³×C₁₉
prime radical	C₁₉×#3292	C₂
LCS	G ▷ #127 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#127 ◁ G

408 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,29)(22,30,33,34)(23,24,28,35)(26,32,27,31);(20,22)(21,26)(23,31)(24,30)(25,33)(27,29)(28,32)(34,35);(20,22)(21,27)(23,34)(24,32)(25,33)(26,29)(28,30)(31,35)

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6663);