C₁₉×#7235 #18013194

order	4864
nilpotency class	4
isoclinism	isoclinic class of #7221
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7235

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#340
commutator	C₂×C₈	C₄²×C₁₉
Frattini, cosocle	C₂³×C₈	C₂²×C₁₉
prime radical	C₂⁴×C₁₉	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

286 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 1216

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)(22,26,27,24)(23,25)(29,33)(30,37)(31,38)(34,36)(35,42)(39,43)(40,41);(20,22)(21,24)(23,27)(25,26)(28,29,30,34,38,40,43,41,32,36,39,33,31,35,37,42)

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 223);