Finite Group Databasebeta

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C3×D3955 #37557534

order23730
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D3955
unambiguous semidirect productC5⋊(C3×D791)
unambiguous semidirect productC113⋊(C3×D35)

Splittings

Fitting, socle, HallC3×C5×C7×C113 ⋊ C2
derived, HallC5×C7×C113 ⋊ C2×C3
HallC3×C7×C113 ⋊ D5
HallC3×C5×C113 ⋊ D7
HallC7×C113 ⋊ C3×D5
HallC5×C113 ⋊ C3×D7
HallC3×C113 ⋊ D35
SylowC113 ⋊ C3×D35
HallC3×C5×C7 ⋊ D113
HallC5×C7 ⋊ C3×D113
HallC3×C7 ⋊ D565
HallC3×C5 ⋊ D791
SylowC7 ⋊ C3×D565
SylowC5 ⋊ C3×D791

Subgroups

subgroupG/H
center, hypercenterC3D3955
commutator, cosocle, hypocenterC5×C7×C113C2×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C113C2
LCSG ▷ C5×C7×C113
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 128
transitive degreeμt(G) = 11865

A minimal faithful permutation representation — 2 generators on 128 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);(5,8)(6,7)(10,15)(11,14)(12,13)(17,128)(18,127)(19,126)(20,125)(21,124)(22,123)(23,122)(24,121)(25,120)(26,119)(27,118)(28,117)(29,116)(30,115)(31,114)(32,113)(33,112)(34,111)(35,110)(36,109)(37,108)(38,107)(39,106)(40,105)(41,104)(42,103)(43,102)(44,101)(45,100)(46,99)(47,98)(48,97)(49,96)(50,95)(51,94)(52,93)(53,92)(54,91)(55,90)(56,89)(57,88)(58,87)(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)(66,79)(67,78)(68,77)(69,76)(70,75)(71,74)(72,73)

Conjugacy classes & character table

5937 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23730, 10);