C₁₉×#11443 #18017402

order	4864
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#11443

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₂²⋊C₈
prime radical	C₂⁴×C₁₉	M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

382 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 59
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 3 generators on 59 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)(28,29,32,38,33,39,47,56,34,36,48,52,31,37,45,54)(30,40,42,57,41,50,58,55,43,53,46,59,44,35,49,51);(20,22,23,27)(21,24,25,26)(28,30)(29,35)(31,44)(32,46)(33,41)(34,43)(36,50)(37,53)(38,55)(39,40)(42,48)(45,58)(47,49)(51,52)(54,57)(56,59);(29,36)(35,50)(37,39)(38,52)(40,53)(51,55)(54,56)(57,59)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4431);