C₁₉×#11522 #18017481

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11522
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#11522

Subgroups

	subgroup	G/H
center	C₄×C₁₉	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
socle	C₂×C₁₉	#1464
prime radical	C₂⁴×C₁₉	M₁₆
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₉ ◁ C₄²×C₁₉ ◁ C₄×M₁₆×C₁₉ ◁ G

284 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

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

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4510);