C₁₉×#7496 #18013455

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7493
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7496

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1390
commutator	C₂×D₄	C₄²×C₁₉
Frattini, cosocle	#532	C₂²×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₂×D₄ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#532 ◁ G

274 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 66 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 — 2 generators on 35 points:

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

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 484);