C₁₉×#12889 #18018848

order	4864
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#12889

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

310 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 174 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) = 63
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 3 generators on 63 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,29)(27,28)(30,31)(32,33)(34,46)(35,40)(36,54)(37,57)(38,58)(39,45)(41,50)(42,47)(43,56)(44,55)(48,60)(49,59)(51,63)(52,62)(53,61);(25,28)(29,31)(32,34,47,52,38,49,56,53,39,50,37,48,55,51,36,35)(33,40,54,63,44,60,57,41,45,61,43,59,58,62,42,46);(24,26,27,30)(25,29,28,31)(32,35,36,51,55,48,37,50,39,53,56,49,38,52,47,34)(33,41,42,60,58,63,43,40,45,46,57,62,44,59,54,61)

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5877);