C₂×C₁₉×#401 #14560257

order	2432
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₁₉×#401

Subgroups

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

516 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);(5,9)(7,10)(12,15)(16,17)(19,20,22,24)(21,25,26,23);(3,4,6,8)(5,10,9,7)(11,12,14,15)(13,17,18,16)(19,20)(21,25)(22,24)(23,26);(3,5)(4,7)(6,9)(8,10)(11,13,14,18)(12,16,15,17)(19,21,22,26)(20,23,24,25)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×C₁₉×#401, C₁₉×#14251, C₁₉×#14333, …
maximal normal subgroup of	C₄×C₁₉×#401, C₁₉×#14251, C₁₉×#14333, …
maximal quotient of	C₂×C₁₉×#1443, C₄×C₁₉×#401, C₁₉×C₂²⋊#401, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1132);

C2×C19×#401 #14560257

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×C₁₉×#401 #14560257