C₁₉×#7308 #18013267

order	4864
nilpotency class	4
isoclinism	isoclinic class of #7307
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#7308

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#342
commutator	C₂²×C₄	C₄²×C₁₉
Frattini, cosocle	C₂³×Q₈	C₂²×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁴×C₁₉ ◁ C₂³×Q₈×C₁₉ ◁ G

518 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 43
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,25)(24,27)(28,29,31,35,32,36,40,43)(30,34,37,42,38,33,39,41);(20,22)(21,24,25,26)(23,27)(29,33,36,34)(35,42,43,41)

Conjugacy classes & character table

646 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 296);