C₁₉×#7525 #18013484

order	4864
nilpotency class	6
isoclinism	isoclinic class of #7523
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7525

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#1404
commutator	#125	C₂×C₄×C₁₉
Frattini, cosocle	#491	C₂²×C₁₉
prime radical	C₁₉×#562	C₄
LCS	G ▷ #125 ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₄²×C₁₉ ◁ C₁₉×#491 ◁ G

138 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 30 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)(20,21,23,27,24,29,35,45)(22,30,32,43,31,41,48,50)(25,28,39,46,37,47,36,44)(26,34,40,38,42,49,51,33);(21,26)(22,31)(25,37)(27,43)(28,41)(29,42)(30,47)(34,49)(36,39)(40,46)(44,51)(45,50)

Conjugacy classes & character table

361 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 513);