C₃×C₇⋊D₉₁₇ #50310062

order	38514
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₃×C₇⋊D₉₁₇
unambiguous semidirect product	C₁₃₁⋊(C₃×C₇⋊D₇)

Splittings

Fitting, socle, Hall	C₃×C₇²×C₁₃₁ ⋊ C₂
derived, Hall	C₇²×C₁₃₁ ⋊ C₂×C₃
Hall	C₃×C₁₃₁ ⋊ C₇⋊D₇
Hall	C₃×C₇² ⋊ D₁₃₁
Sylow	C₁₃₁ ⋊ C₃×C₇⋊D₇
Sylow	C₇² ⋊ C₃×D₁₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₇⋊D₉₁₇
commutator, cosocle, hypocenter	C₇²×C₁₃₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃₁	C₂
LCS	G ▷ C₇²×C₁₃₁
UCS	C₁ ◁ C₃

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 148
transitive degree	μ_t(G) = 19257

A minimal faithful permutation representation — 3 generators on 148 points:

(1,2,3)(5,6)(7,8)(9,10)(12,13)(14,15)(16,17)(19,20)(21,22)(23,24)(25,26)(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)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96)(97,98)(99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148);(11,12,14,16,17,15,13)(18,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131,133,135,137,139,141,143,145,147,148,146,144,142,140,138,136,134,132,130,128,126,124,122,120,118,116,114,112,110,108,106,104,102,100,98,96,94,92,90,88,86,84,82,80,78,76,74,72,70,68,66,64,62,60,58,56,54,52,50,48,46,44,42,40,38,36,34,32,30,28,26,24,22,20);(4,5,7,9,10,8,6)

Conjugacy classes & character table

9633 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38514, 40);

C3×C7⋊D917 #50310062