Finite Group Databasebeta

← Prev (#44538955) Next (#44538957) →

D77×C41⋊C5 #44538956

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

Aliases

direct productD77×C41⋊C5
unambiguous semidirect productC7⋊(D11×C41⋊C5)

Splittings

Fitting, socle, derived, HallC7×C11×C41 ⋊ C2×C5
HallC7×C11×C41⋊C5 ⋊ C2
HallC41×D77 ⋊ C5
HallC11×C41⋊C5 ⋊ D7
HallC7×C41⋊C5 ⋊ D11
HallC11×C41 ⋊ C5×D7
HallC7×C41 ⋊ C5×D11
HallC7×C11 ⋊ C2×C41⋊C5
SylowC41 ⋊ C5×D77
SylowC11 ⋊ D7×C41⋊C5
SylowC7 ⋊ D11×C41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C11×C41C2×C5
LCSG ▷ C7×C11×C41
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3157

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31570, 53);