C₃×C₁₁⋊D₄₇₃ #44530218

order	31218
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁₁

Aliases

direct product	C₃×C₁₁⋊D₄₇₃
unambiguous semidirect product	C₁₁⋊(C₃×D₄₇₃)

Splittings

Fitting, socle, Hall	C₃×C₁₁²×C₄₃ ⋊ C₂
derived, Hall	C₁₁²×C₄₃ ⋊ C₂×C₃
Hall	C₃×C₁₁² ⋊ D₄₃
Hall	C₃×C₄₃ ⋊ C₁₁⋊D₁₁
Sylow	C₁₁² ⋊ C₃×D₄₃
Sylow	C₄₃ ⋊ C₃×C₁₁⋊D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₁₁⋊D₄₇₃
commutator, cosocle, hypocenter	C₁₁²×C₄₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₁²×C₄₃	C₂
LCS	G ▷ C₁₁²×C₄₃
UCS	C₁ ◁ C₃

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 68
transitive degree	μ_t(G) = 15609

A minimal faithful permutation representation — 3 generators on 68 points:

(1,2,3)(5,6)(7,8)(9,10)(11,12)(13,14)(16,17)(18,19)(20,21)(22,23)(24,25)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68);(15,16,18,20,22,24,25,23,21,19,17)(26,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28);(4,5,7,9,11,13,14,12,10,8,6)

Conjugacy classes & character table

7809 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31218, 34);

C3×C11⋊D473 #44530218