C₃×D₃₉₅₉ #37557678

order	23754
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₃₉₅₉
unambiguous semidirect product	C₁₀₇⋊(C₃×D₃₇)

Splittings

Fitting, socle, Hall	C₃×C₃₇×C₁₀₇ ⋊ C₂
derived, Hall	C₃₇×C₁₀₇ ⋊ C₂×C₃
Hall	C₃×C₁₀₇ ⋊ D₃₇
Hall	C₃×C₃₇ ⋊ D₁₀₇
Sylow	C₁₀₇ ⋊ C₃×D₃₇
Sylow	C₃₇ ⋊ C₃×D₁₀₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₃₉₅₉
commutator, cosocle, hypocenter	C₃₇×C₁₀₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₃₇×C₁₀₇	C₂
LCS	G ▷ C₃₇×C₁₀₇
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 147
transitive degree	μ_t(G) = 11877

A minimal faithful permutation representation — 2 generators on 147 points:

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

Conjugacy classes & character table

5943 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23754, 5);

C3×D3959 #37557678