C₁₉×#7448 #18013407

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7447
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7448

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1361
commutator	C₂×C₁₆	C₂×C₄×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
prime radical	C₁₉×#2246	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

146 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 generators on 51 points:

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

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 436);