C₁₉×#33761 #18039720

order	4864
nilpotency class	4
isoclinism	isoclinic class of #33758
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₉×#33761

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

584 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 202 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 — 4 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)(23,25)(24,27)(28,29,33,37)(30,38,39,56)(31,42,46,57)(32,47,44,36)(34,49,50,40)(35,52,54,45)(41,58,48,53)(43,55,59,51);(20,22)(21,24)(23,27)(25,26)(30,39)(34,50)(38,56)(40,49)(41,48)(43,59)(51,55)(53,58);(22,27)(24,26)(28,30,33,39)(29,34,37,50)(31,43,46,59)(32,48,44,41)(35,53,54,58)(36,55,47,51)(38,57,56,42)(40,52,49,45);(21,25)(24,26)

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, 26749);