C₁₉×#13579 #18019538

order	4864
nilpotency class	5
isoclinism	isoclinic class of #13578
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₉×#13579

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	C₂×#353
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	#124	C₂³×C₁₉
prime radical	C₁₉×#3151	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#532 ◁ G

454 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 90 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)(20,21,23,28)(22,26,30,33)(24,27,31,34)(25,29,32,35);(21,26)(22,24)(23,31)(27,29)(30,32)(33,34);(20,22,25,24)(21,26,29,27)(23,30,32,31)(28,33,35,34)

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, 6567);