C₁₃×#907 #11928883

order	1248
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#907

Splittings

Fitting	C₃×C₁₃×M₁₆ ⋊ C₂
Hall	C₃×C₁₃ ⋊ #131
Sylow	C₃ ⋊ C₁₃×#131

Subgroups

	subgroup	G/H
center	C₄×C₁₃	C₂²×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₃
Frattini	C₄	C₂²×D₃×C₁₃
Fitting	C₃×C₁₃×M₁₆	C₂
socle	C₂×C₃×C₁₃	C₂²×C₄
prime radical	C₁₃×#235	C₂
cosocle	C₃×C₄	C₂³×C₁₃
hypercenter	C₁₃×M₁₆	D₃
hypocenter	C₃	C₁₃×#131
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₃ ◁ C₁₃×M₁₆

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 624

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(17,19,20,26,21,25,27,31)(18,23,24,30,22,28,29,32);(18,22)(19,25)(24,29)(26,31);(15,16)(17,18)(19,23)(20,24)(21,22)(25,28)(26,30)(27,29)(31,32)

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, 995);

C13×#907 #11928883