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C2×C7×C3⋊D195 #30655781

order16380
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C7×C3⋊D195
unambiguous semidirect product(C2×C3)⋊(C7×D195)
unambiguous semidirect product(C2×C5)⋊(C7×C3⋊D39)
unambiguous semidirect product(C2×C13)⋊(C7×C3⋊D15)

Splittings

Fitting, socleC2×C32×C5×C7×C13 ⋊ C2
derived, HallC32×C5×C13 ⋊ C22×C7
HallC32×C5×C7×C13 ⋊ C22
HallC32×C7×C13 ⋊ C2×D5
HallC5×C7×C13 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D13
HallC32×C13 ⋊ C2×C7×D5
HallC7×C13 ⋊ C2×C3⋊D15
HallC5×C13 ⋊ C2×C7×C3⋊D3
HallC32×C7 ⋊ C2×D65
HallC32×C5 ⋊ C2×C7×D13
HallC5×C7 ⋊ C2×C3⋊D39
SylowC13 ⋊ C2×C7×C3⋊D15
SylowC32 ⋊ C2×C7×D65
SylowC5 ⋊ C2×C7×C3⋊D39

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊D195
commutator, cosocle, hypocenterC32×C5×C13C22×C7
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C13C2
LCSG ▷ C32×C5×C13
UCSC1 ◁ C2×C7

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 8190

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

4116 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 831);