C₁₉×#11917 #18017876

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11915
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#11917

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1533
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	#97	C₂³×C₁₉
prime radical	C₁₉×#532	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×M₁₆×C₁₉ ◁ G

280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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)(20,21,24,28,23,29,36,47,25,30,40,48,37,27,39,45)(22,31,33,49,34,26,41,43,35,42,50,46,32,44,38,51);(20,22)(21,26)(23,32)(24,38)(25,35)(27,42)(28,46)(29,31)(30,44)(33,39)(34,37)(36,50)(40,41)(43,47)(45,51)(48,49);(20,23,25,37)(21,27,30,29)(22,32,35,34)(24,39,40,36)(26,42,44,31)(28,47,48,45)(33,41,50,38)(43,49,51,46)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4905);