C₁₉×#13684 #18019643

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13681
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13684

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2196
commutator, Frattini, cosocle	C₄⋊Q₈	C₂³×C₁₉
prime radical	C₁₉×#3293	C₂
LCS	G ▷ C₄⋊Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×C₄⋊Q₈ ◁ G

378 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 58 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)(20,21,27,26)(22,31,35,45)(23,36,38,40)(24,25,41,30)(28,39,34,33)(29,42,43,37)(32,44,48,50)(46,49,51,47);(20,22,27,35)(21,28,26,34)(23,32,38,48)(24,39,41,33)(25,31,30,45)(29,44,43,50)(36,49,40,47)(37,51,42,46);(20,23)(21,29)(22,32)(24,40)(25,42)(26,43)(27,38)(28,44)(30,37)(31,46)(33,49)(34,50)(35,48)(36,41)(39,47)(45,51)

Conjugacy classes & character table

475 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 6672);