C₁₉×#12511 #18018470

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12503
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₁₉×#12511

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#493	C₂²
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈²×C₁₉ ◁ G

260 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 67
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28)(23,31)(24,26)(25,29)(27,32)(30,34)(33,35)(36,37)(38,52)(39,45)(40,60)(41,62)(42,50)(43,49)(44,51)(46,57)(47,53)(48,61)(54,64)(55,63)(56,67)(58,65)(59,66);(20,22,23,29,24,30,32,35)(21,25,27,28,26,33,31,34)(36,38,53,58,42,55,61,59,44,57,41,54,43,56,40,39)(37,45,60,67,49,64,62,46,51,66,48,63,50,65,47,52);(21,26)(25,33)(27,31)(28,34)(36,39,40,56,43,54,41,57,44,59,61,55,42,58,53,38)(37,46,47,64,50,67,48,45,51,52,62,65,49,63,60,66)

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5499);