C₁₉×#11814 #18017773

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11796
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#11814

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄⋊C₄×C₁₉ ◁ G

434 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 106 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)(20,21,23,29,25,30,39,47)(22,31,34,46,35,28,37,45)(24,27,38,43,33,44,36,49)(26,40,41,48,42,50,51,32);(21,26,30,42)(22,32)(23,36)(27,31,44,28)(29,46,47,45)(34,37)(35,48)(38,39)(40,50)(41,49,51,43);(21,27)(26,31)(28,42)(29,43)(30,44)(41,46)(45,51)(47,49)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4802);