C₁₉×#11496 #18017455

order	4864
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#11496

Subgroups

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

296 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 67
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 67 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28,30,25)(23,26)(24,27)(29,34,35,32)(31,33)(36,37,41,47,43,46,55,63,42,48,54,64,40,56,39,45)(38,49,52,59,51,44,58,60,53,62,66,67,57,61,50,65);(20,22,24,30)(21,25,27,28)(23,29,31,35)(26,32,33,34)(36,38,42,53)(37,44,48,61)(39,50,55,58)(40,57,43,51)(41,52,54,66)(45,59,63,67)(46,62,56,49)(47,60,64,65);(20,23,24,31)(21,26,27,33)(22,29,30,35)(25,32,28,34)(36,39,40,54,42,55,43,41)(37,45,56,64,48,63,46,47)(38,50,57,66,53,58,51,52)(44,59,49,65,61,67,62,60)

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 4484);