Finite Group Databasebeta

← Prev (#44538961) Next (#44538963) →

C7⋊((C41⋊C5)⋊D11) #44538962

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

Aliases

unambiguous semidirect productC7⋊((C41⋊C5)⋊D11)
unambiguous semidirect product(C41⋊C5)⋊D77

Splittings

Fitting, socle, derived, HallC7×C11×C41 ⋊ C2×C5
HallC7×C11×C41⋊C5 ⋊ C2
HallD3157 ⋊ C5
HallC11×C41⋊C5 ⋊ D7
HallC7×C41⋊C5 ⋊ D11
HallC11×C41 ⋊ C5×D7
HallC7×C41 ⋊ C5×D11
HallC41⋊C5 ⋊ D77
HallC7×C11 ⋊ D41⋊C5
SylowC41 ⋊ C5×D77
SylowC11 ⋊ C7⋊(D41⋊C5)
SylowC7 ⋊ (C41⋊C5)⋊D11

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

Polycyclic presentation:

2,5,7,11,41|c^a=c^6,d^a=d^10,e^a=e^40,e^b=e^10

Conjugacy classes & character table

508 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31570, 59);