C₁₉×#12708 #18018667

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12707
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₉×#12708

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1781
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₁₉×#3487	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

1002 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 146 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)(22,30,33,44)(23,27)(24,36,39,28)(25,29)(26,32)(31,47,49,46)(34,45,38,42)(35,43)(37,41)(40,48)(50,51);(20,22)(21,26)(23,31)(24,37)(25,33)(27,40)(28,44)(29,41)(30,36)(32,39)(34,50)(35,49)(38,48)(42,46)(43,51)(45,47);(20,23,25,35)(21,27,29,43)(22,31,33,49)(24,38,39,34)(26,40,41,51)(28,45,36,42)(30,46,44,47)(32,50,37,48)

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, 5696);