C₁₉×#13683 #18019642

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

Aliases

direct product

C₁₉×#13683

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2196
commutator, Frattini, cosocle	C₄⋊Q₈	C₂³×C₁₉
prime radical	C₁₉×#3291	C₂
LCS	G ▷ C₄⋊Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×C₄⋊Q₈ ◁ G

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

normal subgroups only

This group has 392 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) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,26,25)(22,30,33,35)(23,34,29,24)(27,32,28,31);(20,22)(21,27)(23,32)(24,35)(25,28)(26,33)(29,31)(30,34);(20,22)(21,28)(23,30)(24,31)(25,27)(26,33)(29,35)(32,34)

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, 6671);