Finite Group Databasebeta

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C3×D4345 #39907625

order26070
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D4345
unambiguous semidirect productC5⋊(C3×D869)
unambiguous semidirect productC11⋊(C3×D395)

Splittings

Fitting, socle, HallC3×C5×C11×C79 ⋊ C2
derived, HallC5×C11×C79 ⋊ C2×C3
HallC3×C11×C79 ⋊ D5
HallC3×C5×C79 ⋊ D11
HallC11×C79 ⋊ C3×D5
HallC5×C79 ⋊ C3×D11
HallC3×C79 ⋊ D55
HallC3×C5×C11 ⋊ D79
SylowC79 ⋊ C3×D55
HallC5×C11 ⋊ C3×D79
HallC3×C11 ⋊ D395
HallC3×C5 ⋊ D869
SylowC11 ⋊ C3×D395
SylowC5 ⋊ C3×D869

Subgroups

subgroupG/H
center, hypercenterC3D4345
commutator, cosocle, hypocenterC5×C11×C79C2×C3
FrattiniC1G
Fitting, socleC3×C5×C11×C79C2
LCSG ▷ C5×C11×C79
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 98
transitive degreeμt(G) = 13035

A minimal faithful permutation representation — 2 generators on 98 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);(5,8)(6,7)(10,19)(11,18)(12,17)(13,16)(14,15)(21,98)(22,97)(23,96)(24,95)(25,94)(26,93)(27,92)(28,91)(29,90)(30,89)(31,88)(32,87)(33,86)(34,85)(35,84)(36,83)(37,82)(38,81)(39,80)(40,79)(41,78)(42,77)(43,76)(44,75)(45,74)(46,73)(47,72)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(57,62)(58,61)(59,60)

Conjugacy classes & character table

6522 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26070, 11);