Finite Group Databasebeta

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C7×#17985235 #44538928

order31570
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#17985235

Splittings

Fitting, socle, HallC7×C11×C41 ⋊ C2×C5
derived, HallC11×C41 ⋊ C2×C5×C7
HallC7×#14555919 ⋊ C2
HallC7×C11×D41 ⋊ C5
Hall#14555919 ⋊ C2×C7
HallC11×D41 ⋊ C5×C7
HallC7×D41 ⋊ C11⋊C5
HallC7×C41 ⋊ C2×C11⋊C5
HallD41 ⋊ C7×C11⋊C5
HallC7×C11 ⋊ D41⋊C5
SylowC41 ⋊ C2×C7×C11⋊C5
SylowC11 ⋊ C7×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC7#17985235
commutator, cosocle, hypocenterC11×C41C2×C5×C7
FrattiniC1G
Fitting, socleC7×C11×C41C2×C5
LCSG ▷ C11×C41
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3157

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31570, 25);