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C7×D2475 #46831374

order34650
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D2475
unambiguous semidirect productC9⋊(C7×D275)
unambiguous semidirect productC11⋊(C7×D225)
unambiguous semidirect productC25⋊(C7×D99)

Splittings

Fitting, HallC7×C9×C11×C25 ⋊ C2
derived, HallC9×C11×C25 ⋊ C2×C7
HallC7×C11×C25 ⋊ D9
HallC7×C9×C25 ⋊ D11
HallC7×C9×C11 ⋊ D25
HallC11×C25 ⋊ C7×D9
HallC9×C25 ⋊ C7×D11
HallC7×C25 ⋊ D99
HallC9×C11 ⋊ C7×D25
HallC7×C11 ⋊ D225
HallC7×C9 ⋊ D275
SylowC25 ⋊ C7×D99
SylowC11 ⋊ C7×D225
SylowC9 ⋊ C7×D275

Subgroups

subgroupG/H
center, hypercenterC7D2475
commutator, cosocle, hypocenterC9×C11×C25C2×C7
FrattiniC3×C5C7×D165
FittingC7×C9×C11×C25C2
socleC3×C5×C7×C11D15
LCSG ▷ C9×C11×C25
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 17325

A minimal faithful permutation representation — 2 generators on 52 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);(9,16)(10,15)(11,14)(12,13)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(43,52)(44,51)(45,50)(46,49)(47,48)

Conjugacy classes & character table

8673 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 17);