C₁₉×#7452 #18013411

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7418
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#7452

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₉	#357
commutator	C₂×C₁₆	C₂×C₄×C₁₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₉
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₄×C₁₆×C₁₉ ◁ G

102 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 4864

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

Conjugacy classes & character table

931 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 440);