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C3×D4355 #39908398

order26130
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D4355
unambiguous semidirect productC5⋊(C3×D871)

Splittings

Fitting, socle, HallC3×C5×C13×C67 ⋊ C2
derived, HallC5×C13×C67 ⋊ C2×C3
HallC3×C13×C67 ⋊ D5
HallC3×C5×C67 ⋊ D13
HallC13×C67 ⋊ C3×D5
HallC5×C67 ⋊ C3×D13
HallC3×C67 ⋊ D65
HallC3×C5×C13 ⋊ D67
SylowC67 ⋊ C3×D65
HallC5×C13 ⋊ C3×D67
HallC3×C13 ⋊ D335
HallC3×C5 ⋊ D871
SylowC13 ⋊ C3×D335
SylowC5 ⋊ C3×D871

Subgroups

subgroupG/H
center, hypercenterC3D4355
commutator, cosocle, hypocenterC5×C13×C67C2×C3
FrattiniC1G
Fitting, socleC3×C5×C13×C67C2
LCSG ▷ C5×C13×C67
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 88
transitive degreeμt(G) = 13065

A minimal faithful permutation representation — 2 generators on 88 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);(5,8)(6,7)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)(23,88)(24,87)(25,86)(26,85)(27,84)(28,83)(29,82)(30,81)(31,80)(32,79)(33,78)(34,77)(35,76)(36,75)(37,74)(38,73)(39,72)(40,71)(41,70)(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)(54,57)(55,56)

Conjugacy classes & character table

6537 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26130, 12);