C₁₉×#12845 #18018804

order	4864
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#12845

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₁₉	C₂³
commutator	C₂³	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂³×C₁₉	C₂²×C₈
prime radical	C₂⁴×C₁₉	C₂×C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₉ ◁ G

454 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 182 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) = 2432

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)(32,33,35,39,36,40,45,51,37,41,46,52,47,53,57,61)(34,38,43,49,44,50,56,60,42,48,54,58,55,59,62,63);(25,28)(29,31)(32,34)(33,38)(35,43)(36,44)(37,42)(39,49)(40,50)(41,48)(45,56)(46,54)(47,55)(51,60)(52,58)(53,59)(57,62)(61,63);(21,23)(24,26,27,30)(25,29,28,31)(34,42)(38,48)(43,54)(44,55)(49,58)(50,59)(56,62)(60,63)

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, 5833);