C₃×D₂₀₈ #11928030

order	1248
isoclinism	isoclinic class of D₂₀₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₃×D₂₀₈

Splittings

Fitting	C₃×C₁₃×C₁₆ ⋊ C₂
Hall	C₃×C₁₃ ⋊ D₁₆
Sylow	C₁₃ ⋊ C₃×D₁₆

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
hypercenter	C₃×C₁₆	D₁₃
hypocenter	C₁₃	C₃×D₁₆
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×C₁₆

56 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)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32);(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)(21,32)(22,31)(23,30)(24,29)(25,28)(26,27)

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, 142);

C3×D208 #11928030