C₁₉×#1324 #14559181

order	2432
nilpotency class	4
isoclinism	isoclinic class of #353
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#1324

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#99
commutator	C₂×C₄	C₂×C₈×C₁₉
Frattini, cosocle	C₂×C₄⋊C₄	C₂²×C₁₉
prime radical	C₂³×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₁₉ ◁ C₂×C₄⋊C₄×C₁₉ ◁ G

118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 2 generators on 43 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7352, C₁₉×#7353, C₁₉×#7359, …
maximal normal subgroup of	C₁₉×#7352, C₁₉×#7353, C₁₉×#7359, …
maximal quotient of	C₁₉×#7062, C₁₉×#7065, C₁₉×#7122, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 56);

C19×#1324 #14559181

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1324 #14559181