C₂×C₁₉×#1745 #18026321

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₉ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂×C₁₉×#1745

Subgroups

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

1310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 4864

A minimal faithful permutation representation — 4 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);(7,8)(9,12)(10,11)(13,14)(15,16,17,20,18,19,21,22);(3,4,5,6)(8,11)(12,14);(7,9,10,13)(8,12,11,14)(16,19)(20,22)

Conjugacy classes & character table

2128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 13350);

C2×C19×#1745 #18026321

Aliases

Subgroups

Presentation

Conjugacy classes & character table

GAP

C₂×C₁₉×#1745 #18026321