C₁₉×#7319 #18013278

order	4864
nilpotency class	4
isoclinism	isoclinic class of #7318
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#7319

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1304
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 ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

456 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 2 generators on 51 points:

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

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 307);