Finite Group Databasebeta

← Prev (#41031204) Next (#41031206) →

C7×D25×D13⋊C3 #41031205

order27300
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D25×D13⋊C3
unambiguous semidirect productD13⋊(C3×C7×D25)
unambiguous semidirect product(D13×D25)⋊(C3×C7)
unambiguous semidirect product(C25×D13⋊C3)⋊(C2×C7)
unambiguous semidirect product(C13⋊C3×D25)⋊(C2×C7)
unambiguous semidirect product(C25⋊(D13⋊C3))⋊(C2×C7)

Splittings

Fitting, HallC7×C13×C25 ⋊ C22×C3
derived, HallC13×C25 ⋊ C22×C3×C7
HallC7×D13×D25 ⋊ C3
HallC7×C25×C13⋊C3 ⋊ C22
HallD13×D25 ⋊ C3×C7
HallC25×C13⋊C3 ⋊ C22×C7
HallC7×C13⋊C3 ⋊ C2×D25
HallC7×C25 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C2×C3×D25
HallC13⋊C3 ⋊ C2×C7×D25
SylowC25 ⋊ C2×C7×D13⋊C3
SylowC13 ⋊ C2×C3×C7×D25

Subgroups

subgroupG/H
center, hypercenterC7D25×D13⋊C3
commutator, cosocle, hypocenterC13×C25C22×C3×C7
FrattiniC5C7×D5×D13⋊C3
FittingC7×C13×C25C22×C3
socleC5×C7×C13C2×C3×D5
LCSG ▷ C13×C25
UCSC1 ◁ C7

120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2275

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 95);