C₁₉×#12376 #18018335

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12376

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₁₉×#3273	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#436 ◁ G

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

normal subgroups only

This group has 366 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) = 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)(20,21,24,27)(22,25,23,26)(28,29,33,37)(30,38,40,56)(31,42,44,58)(32,47,45,36)(34,49,50,39)(35,52,54,46)(41,57,48,53)(43,55,59,51);(21,25)(22,23)(26,27)(28,30)(29,34)(31,43)(32,48)(33,40)(35,53)(36,55)(37,50)(38,42)(39,46)(41,45)(44,59)(47,51)(49,52)(54,57)(56,58);(21,26)(22,23)(25,27)(31,44)(35,54)(38,56)(39,49)(42,58)(43,59)(46,52)(53,57)

Conjugacy classes & character table

589 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5364);