C₁₃×#948 #11928924

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

Aliases

direct product

C₁₃×#948

Splittings

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, prime radical	C₃×C₁₃×#41	C₂
socle	C₂×C₃×C₁₃	C₂²×C₄
cosocle	C₃×C₄	C₂³×C₁₃
hypercenter	C₁₃×#41	D₃
hypocenter	C₃	C₁₃×#131
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₁₃ ◁ C₁₃×#41

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)(19,25)(22,28)(26,31)(29,32);(17,19)(18,22)(20,26)(21,25)(23,29)(24,28)(27,31)(30,32);(15,16)(17,18,20,23,21,24,27,30)(19,22,26,29,25,28,31,32)

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, 1036);

C13×#948 #11928924