C₁₉×#2153 #14560010

order	2432
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#2153

Subgroups

	subgroup	G/H
center	C₈×C₁₉	C₂×D₄
commutator	C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂×C₈	C₂³×C₁₉
socle	C₂×C₁₉	C₂×C₄⋊C₈
prime radical	C₂³×C₁₉	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₉ ◁ C₂²×C₈×C₁₉ ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,29,25,28,38,43,26,30,39,44,23,36,37,49)(22,31,34,46,35,41,48,50,32,45,47,51,33,27,40,42);(20,22,23,33,26,32,25,35)(21,27,28,31,30,41,36,45)(24,34,37,40,39,47,38,48)(29,42,43,46,44,50,49,51);(22,32)(27,41)(31,45)(33,35)(34,47)(40,48)(42,50)(46,51)

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#11989, C₁₉×#11990, C₁₉×#11991, …
maximal normal subgroup of	C₁₉×#11989, C₁₉×#11990, C₁₉×#11991, …
maximal quotient of	C₁₉×#11997, C₁₉×#12005, C₁₉×#12014, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 885);

C19×#2153 #14560010

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#2153 #14560010