C₂×C₁₉×#485 #14560945

order	2432
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×C₁₉×#485

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
prime radical	C₂⁴×C₁₉	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

416 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1216

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);(3,4)(5,8)(6,7)(9,10)(11,12,15,19)(13,16,21,25)(14,17,22,18)(20,23,26,24);(4,7)(8,10)(11,13,15,21)(12,16,19,25)(14,20,22,26)(17,23,18,24);(3,5,6,9)(4,8,7,10)(12,17)(14,22)(16,23)(18,19)(20,26)(24,25)

Conjugacy classes & character table

722 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9240, C₄×C₁₉×#485, C₁₉×#21583, …
maximal normal subgroup of	C₁₉×#9240, C₄×C₁₉×#485, C₁₉×#21583, …
maximal quotient of	C₂×C₁₉×#1825, C₂×C₁₉×#1854, C₂×C₁₉×#1873, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1820);

C2×C19×#485 #14560945

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×#485 #14560945