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C₁₉×#1410 #14559267

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

Aliases

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#353
commutator	C₄²	C₂×C₄×C₁₉
Frattini, cosocle	C₄⋊Q₈	C₂²×C₁₉
prime radical	C₁₉×#127	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₁₉×C₄⋊Q₈ ◁ G

104 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)(20,21,22,27,24,28,31,35)(23,25,29,33,32,26,30,34);(21,25)(22,29)(23,32)(26,28)(30,31)(33,34)

Conjugacy classes & character table

323 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₉×#7517, C₁₉×#7518, C₁₉×#7527, …
maximal normal subgroup of	C₁₉×#7517, C₁₉×#7518, C₁₉×#7527, …
maximal quotient of	C₁₉×#7354, C₁₉×#7371, C₁₉×#7404, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2432, 142);