C₁₉×#32857 #18038816

order	4864
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#32857

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₁₉×#376 ◁ G

510 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 206 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) = 4864

A minimal faithful permutation representation — 4 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22)(25,26)(28,29,32,35)(30,36,38,33)(31,34,40,43)(37,42,39,41)(44,45,47,49)(46,52,54,50)(48,51,55,57)(53,58,56,59);(20,21,24,22)(23,25,27,26)(28,30,32,38)(29,33,35,36)(31,39,40,37)(34,42,43,41)(45,49)(46,53)(48,55)(50,58)(52,59)(54,56);(20,22,24,21)(23,25,27,26)(31,40)(34,43)(37,39)(41,42)(44,46,47,54)(45,50,49,52)(48,56,55,53)(51,58,57,59);(20,23,24,27)(21,25,22,26)(28,31,32,40)(29,34,35,43)(30,37,38,39)(33,41,36,42)(45,49)(46,54)(51,57)(53,56)

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, 25845);