Finite Group Databasebeta

← Prev (#11926040) Next (#11926042) →

C₁₉×#365 #11926041

order	1216
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#106
commutator	C₈	C₂×C₄×C₁₉
Frattini, cosocle	C₂×C₈	C₂²×C₁₉
prime radical	C₂²×C₁₉	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×C₈×C₁₉ ◁ G

42 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)(21,25,26,31)(22,28)(23,30)(27,34,33,32)(29,35);(20,21,22,25,23,27,28,32,24,26,29,31,30,33,35,34)

Conjugacy classes & character table

304 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₉×#365, #14565406, #14565525, …
maximal subgroup of	C₂×C₁₉×#365, C₁₉×#2155, C₁₉×#2180, …
maximal normal subgroup of	C₂×C₁₉×#365, C₁₉×#2155, C₁₉×#2180, …
maximal quotient of	C₁₉×#1368, C₁₉×#1383, C₂×C₁₉×#365

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1216, 46);