Finite Group Databasebeta

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C5×D3157 #44538917

order31570
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3157
unambiguous semidirect productC7⋊(C5×D451)

Splittings

Fitting, socle, HallC5×C7×C11×C41 ⋊ C2
derived, HallC7×C11×C41 ⋊ C2×C5
HallC5×C11×C41 ⋊ D7
HallC5×C7×C41 ⋊ D11
HallC11×C41 ⋊ C5×D7
HallC5×C7×C11 ⋊ D41
HallC7×C41 ⋊ C5×D11
HallC5×C41 ⋊ D77
HallC7×C11 ⋊ C5×D41
HallC5×C11 ⋊ D287
SylowC41 ⋊ C5×D77
HallC5×C7 ⋊ D451
SylowC11 ⋊ C5×D287
SylowC7 ⋊ C5×D451

Subgroups

subgroupG/H
center, hypercenterC5D3157
commutator, cosocle, hypocenterC7×C11×C41C2×C5
FrattiniC1G
Fitting, socleC5×C7×C11×C41C2
LCSG ▷ C7×C11×C41
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15785

Conjugacy classes & character table

7900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31570, 14);