C₁₉×#7390 #18013349

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×#7390

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1333
commutator	C₁₆	C₂×C₈×C₁₉
Frattini, cosocle	#346	C₂²×C₁₉
prime radical	C₂×C₁₉×D₁₆	C₄
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄×C₈×C₁₉ ◁ C₁₉×#346 ◁ G

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

normal subgroups only

This group has 128 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)(20,21,23,30,25,32,36,50,27,33,42,31,26,44,24,43)(22,34,35,48,38,28,37,45,40,46,41,49,39,47,51,29);(21,28)(22,35)(23,24)(25,26)(29,43)(30,49)(31,48)(32,34)(33,47)(36,42)(37,39)(38,51)(40,41)(44,46)(45,50)

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, 378);