Finite Group Databasebeta

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C7×D1845 #38788913

order25830
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D1845
unambiguous semidirect productC5⋊(C7×D369)
unambiguous semidirect productC9⋊(C7×D205)
unambiguous semidirect productC41⋊(C7×D45)

Splittings

Fitting, HallC5×C7×C9×C41 ⋊ C2
derived, HallC5×C9×C41 ⋊ C2×C7
HallC7×C9×C41 ⋊ D5
HallC5×C7×C41 ⋊ D9
HallC9×C41 ⋊ C7×D5
HallC5×C7×C9 ⋊ D41
HallC7×C41 ⋊ D45
HallC5×C41 ⋊ C7×D9
HallC7×C9 ⋊ D205
HallC5×C9 ⋊ C7×D41
SylowC41 ⋊ C7×D45
HallC5×C7 ⋊ D369
SylowC9 ⋊ C7×D205
SylowC5 ⋊ C7×D369

Subgroups

subgroupG/H
center, hypercenterC7D1845
commutator, cosocle, hypocenterC5×C9×C41C2×C7
FrattiniC3C7×D615
FittingC5×C7×C9×C41C2
socleC3×C5×C7×C41D3
LCSG ▷ C5×C9×C41
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12915

Conjugacy classes & character table

6468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 17);