C₁₉×#13607 #18019566

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13605
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13607

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2127
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	#124	C₂³×C₁₉
prime radical	C₁₉×#535	C₂²
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#535 ◁ G

332 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

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

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, 6595);