C₁₉×#8323 #18014282

order	4864
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#8323

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

930 conjugacy classes of subgroups; only the 214 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 214 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 — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,24,23,25,26,27)(28,29)(30,38)(31,42,44,35)(32,45)(33,37)(34,40)(36,47)(39,53,55,52)(41,51)(43,50,59,57)(46,49)(48,54,56,58);(28,30,33,41)(29,34,37,49)(31,39,44,55)(32,46,47,40)(35,48,42,56)(36,51,45,38)(43,58,59,54)(50,53,57,52);(28,31)(29,35)(30,39)(32,43)(33,44)(34,48)(36,50)(37,42)(38,52)(40,54)(41,55)(45,57)(46,58)(47,59)(49,56)(51,53)

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 1311);