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C2×C5×D819 #30655182

order16380
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D819
unambiguous semidirect product(C2×C7)⋊(C5×D117)
unambiguous semidirect product(C2×C9)⋊(C5×D91)
unambiguous semidirect product(C2×C13)⋊(C5×D63)

Splittings

FittingC2×C5×C7×C9×C13 ⋊ C2
derived, HallC7×C9×C13 ⋊ C22×C5
HallC5×C7×C9×C13 ⋊ C22
HallC5×C9×C13 ⋊ C2×D7
HallC5×C7×C13 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D13
HallC9×C13 ⋊ C2×C5×D7
HallC7×C13 ⋊ C2×C5×D9
HallC5×C13 ⋊ C2×D63
HallC7×C9 ⋊ C2×C5×D13
HallC5×C9 ⋊ C2×D91
HallC5×C7 ⋊ C2×D117
SylowC13 ⋊ C2×C5×D63
SylowC9 ⋊ C2×C5×D91
SylowC7 ⋊ C2×C5×D117

Subgroups

subgroupG/H
center, hypercenterC2×C5D819
commutator, cosocle, hypocenterC7×C9×C13C22×C5
FrattiniC3C2×C5×D273
FittingC2×C5×C7×C9×C13C2
socleC2×C3×C5×C7×C13D3
LCSG ▷ C7×C9×C13
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 8190

A minimal faithful permutation representation — 2 generators on 36 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16)(17,18)(19,20)(22,24)(23,27)(25,26)(28,29)(30,31,32,33,34);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,17,19,20,18,16)(21,29,24,27,26,25,23,22,28)(35,36)

Conjugacy classes & character table

4110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 232);