C₁₉×#1408 #14559265

order	2432
nilpotency class	5
isoclinism	isoclinic class of #1408
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₉×#1408

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#353
commutator	C₄²	C₂×C₄×C₁₉
Frattini, cosocle	#127	C₂²×C₁₉
prime radical	C₁₉×#493	C₂
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×#127 ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 304

A minimal faithful permutation representation — 2 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)(22,29,30,25)(23,27,33,26)(24,28)(31,34,32,35);(20,22)(21,25)(23,32)(24,31)(26,34)(27,29)(28,35)(30,33)

Conjugacy classes & character table

323 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7515, C₁₉×#7516, C₁₉×#7529, …
maximal normal subgroup of	C₁₉×#7515, C₁₉×#7516, C₁₉×#7529, …
maximal quotient of	C₁₉×#7354, C₁₉×#7370, C₁₉×#7402, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 140);

C19×#1408 #14559265

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₁₉×#1408 #14559265