Finite Group Databasebeta

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C7×D2465 #46828512

order34510
automorphism?
homologyAbelianization (H1) = C2×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D2465
unambiguous semidirect productC5⋊(C7×D493)
unambiguous semidirect productC17⋊(C7×D145)

Splittings

Fitting, socle, HallC5×C7×C17×C29 ⋊ C2
derived, HallC5×C17×C29 ⋊ C2×C7
HallC7×C17×C29 ⋊ D5
HallC5×C7×C29 ⋊ D17
HallC5×C7×C17 ⋊ D29
HallC17×C29 ⋊ C7×D5
HallC7×C29 ⋊ D85
HallC5×C29 ⋊ C7×D17
HallC7×C17 ⋊ D145
HallC5×C17 ⋊ C7×D29
HallC5×C7 ⋊ D493
SylowC29 ⋊ C7×D85
SylowC17 ⋊ C7×D145
SylowC5 ⋊ C7×D493

Subgroups

subgroupG/H
center, hypercenterC7D2465
commutator, cosocle, hypocenterC5×C17×C29C2×C7
FrattiniC1G
Fitting, socleC5×C7×C17×C29C2
LCSG ▷ C5×C17×C29
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17255

Conjugacy classes & character table

8638 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34510, 13);