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C2×C5×D1197 #37561046

order23940
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1197
unambiguous semidirect product(C2×C7)⋊(C5×D171)
unambiguous semidirect product(C2×C9)⋊(C5×D133)
unambiguous semidirect product(C2×C19)⋊(C5×D63)

Splittings

FittingC2×C5×C7×C9×C19 ⋊ C2
derived, HallC7×C9×C19 ⋊ C22×C5
HallC5×C7×C9×C19 ⋊ C22
HallC5×C9×C19 ⋊ C2×D7
HallC5×C7×C19 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D19
HallC9×C19 ⋊ C2×C5×D7
HallC7×C19 ⋊ C2×C5×D9
HallC5×C19 ⋊ C2×D63
HallC7×C9 ⋊ C2×C5×D19
HallC5×C9 ⋊ C2×D133
HallC5×C7 ⋊ C2×D171
SylowC19 ⋊ C2×C5×D63
SylowC9 ⋊ C2×C5×D133
SylowC7 ⋊ C2×C5×D171

Subgroups

subgroupG/H
center, hypercenterC2×C5D1197
commutator, cosocle, hypocenterC7×C9×C19C22×C5
FrattiniC3C2×C5×D399
FittingC2×C5×C7×C9×C19C2
socleC2×C3×C5×C7×C19D3
LCSG ▷ C7×C9×C19
UCSC1 ◁ C2×C5

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)(25,26)(28,30)(29,33)(31,32)(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)(20,21,23,25,26,24,22)(27,35,30,33,32,31,29,28,34)(41,42)

Conjugacy classes & character table

6000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 178);