C₁₉×#7309 #18013268

order	4864
nilpotency class	4
isoclinism	isoclinic class of #7307
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#7309

Subgroups

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

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

normal subgroups only

This group has 470 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)(30,38,40,49)(31,42,44,35)(32,36)(33,37)(34,39)(41,53,56,59)(43,48)(45,52,54,50)(46,51)(47,55)(57,58);(20,22)(21,24,25,26)(23,27)(28,30,32,41,33,40,46,56)(29,34,36,47,37,48,51,58)(31,43,45,57,44,39,54,55)(35,49,50,59,42,38,52,53)

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, 297);