Finite Group Databasebeta

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C11×D7×C41⋊C5 #44538944

order31570
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D7×C41⋊C5
unambiguous semidirect productC7⋊(C2×C11×C41⋊C5)
unambiguous semidirect product(D7×C41)⋊(C5×C11)

Splittings

Fitting, socle, HallC7×C11×C41 ⋊ C2×C5
derived, HallC7×C41 ⋊ C2×C5×C11
HallC7×C11×C41⋊C5 ⋊ C2
HallC11×D7×C41 ⋊ C5
HallC7×C41⋊C5 ⋊ C2×C11
HallD7×C41 ⋊ C5×C11
HallC11×C41 ⋊ C5×D7
HallC7×C11 ⋊ C2×C41⋊C5
SylowC41 ⋊ C5×C11×D7
SylowC7 ⋊ C2×C11×C41⋊C5

Subgroups

subgroupG/H
center, hypercenterC11D7×C41⋊C5
commutator, cosocle, hypocenterC7×C41C2×C5×C11
FrattiniC1G
Fitting, socleC7×C11×C41C2×C5
LCSG ▷ C7×C41
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3157

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31570, 41);