C₁₉×#7284 #18013243

order	4864
nilpotency class	4
isoclinism	isoclinic class of #1343
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₉×#7284

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	#99
commutator	C₂²×C₄	C₄²×C₁₉
Frattini, cosocle	C₂×C₄×Q₈	C₂²×C₁₉
socle	C₂²×C₁₉	#342
prime radical	C₂³×C₁₉	#95
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

298 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 43
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 2 generators on 43 points:

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

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 272);