C₂×C₁₉×#2380 #18040303

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₁₉ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product

C₂×C₁₉×#2380

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂²×C₁₉×#127	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

3798 conjugacy classes of subgroups; only the 1486 normal subgroups are shown.

normal subgroups only

This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 1486 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) = 41
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 5 generators on 41 points:

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

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, 27332);