C₁₉×#7044 #18013003

order	4864
nilpotency class	3
isoclinism	isoclinic class of #7035
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#7044

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	#95
commutator	C₂²×C₄	C₄²×C₁₉
Frattini, cosocle	C₂²×C₄²	C₂²×C₁₉
prime radical	C₂⁴×C₁₉	C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

352 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 51
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 2 generators on 51 points:

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

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, 32);