C₁₉×#7334 #18013293

order	4864
nilpotency class	3
isoclinism	isoclinic class of #99
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₃₂ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7334

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₉	C₂²⋊C₄
commutator	C₂²	C₂×C₁₉×C₃₂
Frattini, cosocle	C₂²×C₁₆	C₂²×C₁₉
socle	C₂²×C₁₉	C₂²⋊C₁₆
prime radical	C₂⁴×C₁₉	C₁₆
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₉ ◁ C₂²×C₁₆×C₁₉ ◁ G

182 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 2 generators on 59 points:

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

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, 322);