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C2×C7×D855 #37561044

order23940
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D855
unambiguous semidirect product(C2×C5)⋊(C7×D171)
unambiguous semidirect product(C2×C9)⋊(C7×D95)
unambiguous semidirect product(C2×C19)⋊(C7×D45)

Splittings

FittingC2×C5×C7×C9×C19 ⋊ C2
derived, HallC5×C9×C19 ⋊ C22×C7
HallC5×C7×C9×C19 ⋊ C22
HallC7×C9×C19 ⋊ C2×D5
HallC5×C7×C19 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D19
HallC9×C19 ⋊ C2×C7×D5
HallC7×C19 ⋊ C2×D45
HallC5×C19 ⋊ C2×C7×D9
HallC7×C9 ⋊ C2×D95
HallC5×C9 ⋊ C2×C7×D19
HallC5×C7 ⋊ C2×D171
SylowC19 ⋊ C2×C7×D45
SylowC9 ⋊ C2×C7×D95
SylowC5 ⋊ C2×C7×D171

Subgroups

subgroupG/H
center, hypercenterC2×C7D855
commutator, cosocle, hypocenterC5×C9×C19C22×C7
FrattiniC3C2×C7×D285
FittingC2×C5×C7×C9×C19C2
socleC2×C3×C5×C7×C19D3
LCSG ▷ C5×C9×C19
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 42
transitive degreeμt(G) = 11970

A minimal faithful permutation representation — 2 generators on 42 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(21,22)(23,24)(26,28)(27,31)(29,30)(32,33)(34,35,36,37,38,39,40);(1,2,4,6,8,10,12,14,16,18,19,17,15,13,11,9,7,5,3)(20,21,23,24,22)(25,33,28,31,30,29,27,26,32)(41,42)

Conjugacy classes & character table

6006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 176);