C₁₉×#7306 #18013265

order	4864
nilpotency class	4
isoclinism	isoclinic class of #7304
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#7306

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#342
commutator	C₂⁴	C₄²×C₁₉
Frattini, cosocle	C₂²×#41	C₂²×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂⁴ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

456 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 78 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)(23,25)(24,27)(28,29,32,37,34,39,33,38)(30,40,42,55,44,57,43,56)(31,45,46,54,47,36,48,52)(35,49,50,41,51,58,53,59);(20,22)(21,24,25,26)(23,27)(28,30,33,43,34,44,32,42)(29,35,38,50,39,51,37,53)(31,41,46,58,47,59,48,49)(36,40,52,56,45,57,54,55)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 294);