C₁₉×#3272 #14561129

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₉×#3272

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ G

546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

551 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#19755, C₁₉×#19758, C₁₉×#19803, …
maximal normal subgroup of	C₁₉×#19755, C₁₉×#19758, C₁₉×#19803, …
maximal quotient of	C₁₉×#19883, C₁₉×#19890, C₁₉×#19898, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 2004);

C19×#3272 #14561129

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#3272 #14561129