C₃×D₃₈₇₁ #37551089

order	23226
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×D₃₈₇₁

Splittings

Fitting, Hall	C₃×C₄₉×C₇₉ ⋊ C₂
derived, Hall	C₄₉×C₇₉ ⋊ C₂×C₃
Hall	C₃×C₇₉ ⋊ D₄₉
Hall	C₃×C₄₉ ⋊ D₇₉
Sylow	C₇₉ ⋊ C₃×D₄₉
Sylow	C₄₉ ⋊ C₃×D₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₃₈₇₁
commutator, cosocle, hypocenter	C₄₉×C₇₉	C₂×C₃
Frattini	C₇	C₃×D₅₅₃
Fitting	C₃×C₄₉×C₇₉	C₂
socle	C₃×C₇×C₇₉	D₇
LCS	G ▷ C₄₉×C₇₉
UCS	C₁ ◁ C₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 131
transitive degree	μ_t(G) = 11613

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

Conjugacy classes & character table

5811 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23226, 8);

C3×D3871 #37551089