C₃×C₁₃⋊D₃₇₇ #44440625

order	29406
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁₃

Aliases

direct product	C₃×C₁₃⋊D₃₇₇
unambiguous semidirect product	C₂₉⋊(C₃×C₁₃⋊D₁₃)

Splittings

Fitting, socle, Hall	C₃×C₁₃²×C₂₉ ⋊ C₂
derived, Hall	C₁₃²×C₂₉ ⋊ C₂×C₃
Hall	C₃×C₁₃² ⋊ D₂₉
Sylow	C₁₃² ⋊ C₃×D₂₉
Hall	C₃×C₂₉ ⋊ C₁₃⋊D₁₃
Sylow	C₂₉ ⋊ C₃×C₁₃⋊D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₁₃⋊D₃₇₇
commutator, cosocle, hypocenter	C₁₃²×C₂₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃²×C₂₉	C₂
LCS	G ▷ C₁₃²×C₂₉
UCS	C₁ ◁ C₃

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 14703

A minimal faithful permutation representation — 3 generators on 58 points:

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

Conjugacy classes & character table

7356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29406, 40);

C3×C13⋊D377 #44440625