C₁₉×#14673 #18020632

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

direct product

C₁₉×#14673

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁶×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

2734 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 2734 conjugacy classes of subgroups — too many to draw. Only its 462 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) = 43
transitive degree	μ_t(G) = 1216

A minimal faithful permutation representation — 4 generators on 43 points:

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

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, 7661);