Finite Group Databasebeta

← Prev (#41031818) Next (#41031820) →

C2×C7×D13⋊(C52⋊C3) #41031819

order27300
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C7×D13⋊(C52⋊C3)
unambiguous semidirect productD13⋊(C2×C7×C52⋊C3)
unambiguous semidirect product(C2×D13)⋊(C7×C52⋊C3)

Splittings

Fitting, socleC2×C52×C7×C13 ⋊ C2×C3
derived, HallC52×C13 ⋊ C22×C3×C7
HallC2×C52×C7×D13 ⋊ C3
HallC7×C13⋊(C52⋊C3) ⋊ C22
HallC52×C7×C13 ⋊ C22×C3
HallC2×C52×D13 ⋊ C3×C7
HallC13⋊(C52⋊C3) ⋊ C22×C7
HallC2×C7×D13 ⋊ C52⋊C3
HallC52×C7 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C22×C52⋊C3
HallC2×D13 ⋊ C7×C52⋊C3
SylowC52 ⋊ C2×C7×D13⋊C3
SylowC13 ⋊ C22×C7×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7D13⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C13C22×C3×C7
FrattiniC1G
Fitting, socleC2×C52×C7×C13C2×C3
LCSG ▷ C52×C13
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

1008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 709);