C₂²×C₁₉×#330 #18023593

order	4864
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂²×C₁₉×#330

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₄²	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

1158 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 1158 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) = 39
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 4 generators on 39 points:

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

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, 10622);