Finite Group Databasebeta

← Prev (#41031245) Next (#41031247) →

C2×C25×(C13⋊C3)⋊D7 #41031246

order27300
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×(C13⋊C3)⋊D7
unambiguous semidirect product(C2×C13⋊C3)⋊(D7×C25)

Splittings

FittingC2×C7×C13×C25 ⋊ C2×C3
derived, HallC7×C13 ⋊ C22×C3×C25
HallC2×C25×D91 ⋊ C3
HallC7×C25×C13⋊C3 ⋊ C22
HallC7×C13×C25 ⋊ C22×C3
HallC25×C13⋊C3 ⋊ C2×D7
HallC2×D91 ⋊ C3×C25
HallC13×C25 ⋊ C2×C3×D7
HallC7×C13⋊C3 ⋊ C22×C25
HallC7×C25 ⋊ C2×D13⋊C3
HallC13⋊C3 ⋊ C2×D7×C25
SylowC13 ⋊ C2×C3×D7×C25
SylowC7 ⋊ C2×C25×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C25(C13⋊C3)⋊D7
commutator, hypocenterC7×C13C22×C3×C25
FrattiniC5C2×C5×(C13⋊C3)⋊D7
FittingC2×C7×C13×C25C2×C3
socleC2×C5×C7×C13C2×C3×C5
prime radicalC2×C5×(C13⋊C3)⋊D7C5
cosocleC5×C7×C13C22×C3×C5
LCSG ▷ C7×C13
UCSC1 ◁ C2×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4550

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 136);