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C₁₉×#1309 #14559166

order	2432
nilpotency class	3
isoclinism	isoclinic class of #1304
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₉ · Schur multiplier (H₂) = C₄

Aliases

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#95
commutator	C₂³	C₄²×C₁₉
Frattini, cosocle	C₂×C₄²	C₂²×C₁₉
prime radical	C₂³×C₁₉	C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1216

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)(20,21,22,25,23,24,26,27)(29,32)(30,34);(21,24)(22,26)(28,29,30,33,31,32,34,35)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7414, C₁₉×#7440, C₂×C₁₉×#1309, …
maximal normal subgroup of	C₁₉×#7414, C₁₉×#7440, C₂×C₁₉×#1309, …
maximal quotient of	C₁₉×#7034, C₁₉×#7042, C₁₉×#7050, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 41);