C₁₉×#3217 #14561074

order	2432
nilpotency class	3
isoclinism	isoclinic class of #3192
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#3217

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 ◁ C₂×C₄²×C₁₉ ◁ G

490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 4 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,25)(24,27)(28,29)(30,32)(31,33)(34,35);(20,22,23,27)(21,24,25,26)(29,32)(33,34);(22,27)(24,26)(29,33)(31,35)(32,34);(21,25)(24,26)(29,32)(33,34)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#9340, C₁₉×#9378, C₁₉×#18335, …
maximal normal subgroup of	C₁₉×#9340, C₁₉×#9378, C₁₉×#18335, …
maximal quotient of	C₁₉×#21810, C₁₉×#21867, C₁₉×#21987, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 1949);

C19×#3217 #14561074

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#3217 #14561074