C₁₉×#12046 #18018005

order	4864
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12046

Subgroups

	subgroup	G/H
center	C₁₆×C₁₉	D₈
commutator	C₈	C₂²×C₈×C₁₉
Frattini, cosocle	C₄×C₈	C₂³×C₁₉
socle	C₂×C₁₉	C₈×D₈
prime radical	C₁₉×#508	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₉ ◁ C₂×C₁₆×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 216 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)(20,21,25,31,27,32,43,30,28,33,24,42,26,22,34,36)(23,29,38,45,40,46,51,44,41,47,37,50,39,35,48,49);(20,22)(21,27)(23,35)(24,30)(25,36)(26,33)(28,32)(29,40)(31,43)(34,42)(37,44)(38,49)(39,47)(41,46)(45,51)(48,50);(20,23,25,38,27,40,43,51,28,41,24,37,26,39,34,48)(21,29,31,45,32,46,30,44,33,47,42,50,22,35,36,49)

Conjugacy classes & character table

1672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5034);