C₁₉×#11836 #18017795

order	4864
nilpotency class	4
isoclinism	isoclinic class of #11836
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#11836

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1514
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₉
prime radical	C₁₉×#469	C₂²
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×M₁₆×C₁₉ ◁ G

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

normal subgroups only

This group has 286 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)(22,32,34,49)(23,37,39,44)(24,30)(25,28)(26,31)(27,33)(29,40,46,41)(35,45,36,48)(38,47)(42,51)(43,50);(20,22)(21,27)(23,38)(24,36)(25,35)(26,34)(28,42)(29,45)(30,47)(31,43)(32,37)(33,41)(39,51)(40,50)(44,49)(46,48);(21,28,31,30)(23,39)(27,42,43,47)(29,37,46,44)(32,48,49,45)(33,50)(38,51)(40,41)

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, 4824);