C₃×#88040 #11928029

order	1248
isoclinism	isoclinic class of D₂₀₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×#88040

Splittings

Fitting	C₃×C₁₃×C₁₆ ⋊ C₂
Hall	C₃×C₁₃ ⋊ SD₃₂
Sylow	C₁₃ ⋊ C₃×SD₃₂

Subgroups

	subgroup	G/H
center	C₂×C₃	D₁₀₄
commutator, cosocle	C₈×C₁₃	C₂²×C₃
Frattini	C₈	C₂×C₃×D₁₃
Fitting	C₃×C₁₃×C₁₆	C₂
socle	C₂×C₃×C₁₃	D₈
prime radical	C₃×D₁₀₄	C₂
hypercenter	C₃×C₁₆	D₁₃
hypocenter	C₁₃	C₃×SD₃₂
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×C₁₆

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1248, 141);

C3×#88040 #11928029