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C7×C3⋊D825 #46831451

order34650
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×C3⋊D825
unambiguous semidirect productC3⋊(C7×D825)
unambiguous semidirect productC11⋊(C7×C3⋊D75)
unambiguous semidirect productC25⋊(C7×C3⋊D33)

Splittings

Fitting, HallC32×C7×C11×C25 ⋊ C2
derived, HallC32×C11×C25 ⋊ C2×C7
HallC7×C11×C25 ⋊ C3⋊D3
HallC32×C7×C25 ⋊ D11
HallC32×C7×C11 ⋊ D25
HallC11×C25 ⋊ C7×C3⋊D3
HallC32×C25 ⋊ C7×D11
HallC7×C25 ⋊ C3⋊D33
HallC32×C11 ⋊ C7×D25
HallC7×C11 ⋊ C3⋊D75
HallC32×C7 ⋊ D275
SylowC25 ⋊ C7×C3⋊D33
SylowC11 ⋊ C7×C3⋊D75
SylowC32 ⋊ C7×D275

Subgroups

subgroupG/H
center, hypercenterC7C3⋊D825
commutator, cosocle, hypocenterC32×C11×C25C2×C7
FrattiniC5C7×C3⋊D165
FittingC32×C7×C11×C25C2
socleC32×C5×C7×C11D5
LCSG ▷ C32×C11×C25
UCSC1 ◁ C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 17325

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7)(9,10)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(26,28)(27,31)(29,34)(30,37)(32,40)(33,39)(35,42)(36,44)(38,46)(41,47)(43,48)(45,49);(11,12,13)(14,15,17,19,21,23,24,22,20,18,16)(25,38,42,43,37,27,47,29,49,28,32,39,36,44,33,40,26,45,34,41,31,30,48,35,46);(8,9,10)

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, 94);