C₁₉×#12706 #18018665

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12705
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#12706

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1781
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×D₄	C₂³×C₁₉
prime radical	C₁₉×#3485	C₂
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

1000 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 1000 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)(23,27)(24,36,38,28)(25,29)(26,32,40,50)(31,46)(33,45)(34,43,37,41)(35,42)(39,47,51,49)(44,48);(20,22)(21,26)(23,31)(24,32)(25,33)(27,39)(28,30)(29,40)(34,47)(35,48)(36,45)(37,49)(38,50)(41,46)(42,51)(43,44);(20,23,25,35)(21,27,29,42)(22,31,33,48)(24,37,38,34)(26,39,40,51)(28,43,36,41)(30,44,45,46)(32,49,50,47)

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, 5694);