Finite Group Databasebeta

← Prev (#44473238) Next (#44473240) →

C3×C13×D385 #44473239

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×D385
unambiguous semidirect productC5⋊(C3×C13×D77)
unambiguous semidirect productC11⋊(C3×C13×D35)

Splittings

Fitting, socle, HallC3×C5×C7×C11×C13 ⋊ C2
derived, HallC5×C7×C11 ⋊ C2×C3×C13
HallC5×C7×C11×C13 ⋊ C2×C3
HallC3×C7×C11×C13 ⋊ D5
HallC3×C5×C11×C13 ⋊ D7
HallC3×C5×C7×C13 ⋊ D11
HallC3×C5×C7×C11 ⋊ C2×C13
HallC7×C11×C13 ⋊ C3×D5
HallC5×C11×C13 ⋊ C3×D7
HallC5×C7×C13 ⋊ C3×D11
HallC3×C11×C13 ⋊ D35
HallC3×C7×C13 ⋊ D55
HallC3×C7×C11 ⋊ D5×C13
HallC3×C5×C13 ⋊ D77
HallC3×C5×C11 ⋊ C13×D7
HallC11×C13 ⋊ C3×D35
HallC3×C5×C7 ⋊ C13×D11
HallC7×C13 ⋊ C3×D55
HallC7×C11 ⋊ C3×D5×C13
HallC5×C13 ⋊ C3×D77
HallC5×C11 ⋊ C3×C13×D7
HallC5×C7 ⋊ C3×C13×D11
HallC3×C11 ⋊ C13×D35
HallC3×C7 ⋊ C13×D55
HallC3×C5 ⋊ C13×D77
SylowC11 ⋊ C3×C13×D35
SylowC7 ⋊ C3×C13×D55
SylowC5 ⋊ C3×C13×D77

Subgroups

subgroupG/H
center, hypercenterC3×C13D385
commutator, cosocle, hypocenterC5×C7×C11C2×C3×C13
FrattiniC1G
Fitting, socleC3×C5×C7×C11×C13C2
LCSG ▷ C5×C7×C11
UCSC1 ◁ C3×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15015

Conjugacy classes & character table

7566 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 24);