C₂×C₁₉×#1452 #18023277

order	4864
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₉ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂×C₁₉×#1452

Subgroups

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

902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 4 generators on 45 points:

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

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, 10306);

C2×C19×#1452 #18023277

Aliases

Subgroups

Presentation

Conjugacy classes & character table

GAP

C₂×C₁₉×#1452 #18023277