C₁₃×#875 #11928851

order	1248
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂×C₄

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₁₃×#875

Splittings

Fitting	C₃×C₄²×C₁₃ ⋊ C₂
Hall	C₃×C₁₃ ⋊ #124
Sylow	C₃ ⋊ C₁₃×#124

Subgroups

	subgroup	G/H
center	C₂²×C₁₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₃
Frattini	C₂²	C₂²×D₃×C₁₃
Fitting	C₃×C₄²×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
prime radical	C₂×C₁₃×D₁₂	C₂
hypercenter	C₄²×C₁₃	D₃
hypocenter	C₃	C₁₃×#124
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 624

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(17,19,20,18)(22,26)(25,28);(17,18,20,19)(21,23,24,27)(22,25,26,28);(15,16)(18,19)(21,22)(23,25)(24,26)(27,28)

Conjugacy classes & character table

390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 963);

C13×#875 #11928851