C₃×Dic₁₀₄ #11928031

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

Aliases

direct product

C₃×Dic₁₀₄

Splittings

Hall	C₃×C₁₃ ⋊ Q₃₂
Sylow	C₁₃ ⋊ C₃×Q₃₂

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, prime radical	C₂×C₃×C₁₃	D₈
hypercenter	C₃×C₁₆	D₁₃
hypocenter	C₁₃	C₃×Q₃₂
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×C₁₆

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 1248

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21)(36,37,38,39,40,41,42,43,44,45,46,47,48);(4,20,12,28)(5,21,13,29)(6,22,14,30)(7,23,15,31)(8,24,16,32)(9,25,17,33)(10,26,18,34)(11,27,19,35)(37,48)(38,47)(39,46)(40,45)(41,44)(42,43)

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, 143);

C3×Dic104 #11928031