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C3×D5863 #47976007

order35178
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5863
unambiguous semidirect productC11⋊(C3×D533)
unambiguous semidirect productC41⋊(C3×D143)

Splittings

Fitting, socle, HallC3×C11×C13×C41 ⋊ C2
derived, HallC11×C13×C41 ⋊ C2×C3
HallC3×C13×C41 ⋊ D11
HallC3×C11×C41 ⋊ D13
HallC13×C41 ⋊ C3×D11
HallC11×C41 ⋊ C3×D13
HallC3×C11×C13 ⋊ D41
HallC11×C13 ⋊ C3×D41
HallC3×C41 ⋊ D143
SylowC41 ⋊ C3×D143
HallC3×C13 ⋊ D451
HallC3×C11 ⋊ D533
SylowC13 ⋊ C3×D451
SylowC11 ⋊ C3×D533

Subgroups

subgroupG/H
center, hypercenterC3D5863
commutator, cosocle, hypocenterC11×C13×C41C2×C3
FrattiniC1G
Fitting, socleC3×C11×C13×C41C2
LCSG ▷ C11×C13×C41
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 68
transitive degreeμt(G) = 17589

A minimal faithful permutation representation — 2 generators on 68 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);(5,14)(6,13)(7,12)(8,11)(9,10)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)(29,68)(30,67)(31,66)(32,65)(33,64)(34,63)(35,62)(36,61)(37,60)(38,59)(39,58)(40,57)(41,56)(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)

Conjugacy classes & character table

8799 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35178, 9);