C₁₉×#7253 #18013212

order	4864
nilpotency class	4
isoclinism	isoclinic class of #1343
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7253

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	#99
commutator	C₂²×C₄	C₄²×C₁₉
Frattini, cosocle	C₂×#117	C₂²×C₁₉
socle	C₂²×C₁₉	#342
prime radical	C₂⁴×C₁₉	C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

328 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 102 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)(22,24)(23,26)(25,27)(28,29,32,37,34,39,33,38)(30,40,42,57,44,53,43,58)(31,36,46,54,47,55,48,56)(35,49,50,45,52,59,51,41);(21,24,26,25)(28,30,33,43,34,44,32,42)(29,35,38,51,39,52,37,50)(31,45,46,59,47,41,48,49)(36,53,54,58,55,40,56,57)

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, 241);