C₁₉×#7389 #18013348

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7389
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7389

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1333
commutator	C₁₆	C₂×C₈×C₁₉
Frattini, cosocle	#346	C₂²×C₁₉
prime radical	C₁₉×#508	C₄
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₁₉×#346 ◁ G

118 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 generators on 51 points:

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

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, 377);