Finite Group Databasebeta

← Prev (#44473276) Next (#44473278) →

C5×C13×ΓL(1,𝔽8)×D11 #44473277

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×ΓL(1,𝔽8)×D11
unambiguous semidirect product(C5×C7×D11)⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C11 ⋊ C2×C3×C5×C13
HallC5×C11×C13×ΓL(1,𝔽8) ⋊ C2
HallC5×C7×C13×D11 ⋊ C3
HallC11×C13×ΓL(1,𝔽8) ⋊ C2×C5
HallC7×C13×D11 ⋊ C3×C5
HallC5×C11×ΓL(1,𝔽8) ⋊ C2×C13
HallC7×C11×C13 ⋊ C2×C3×C5
HallC5×C7×D11 ⋊ C3×C13
HallC5×C11×C13 ⋊ C2×ΓL(1,𝔽8)
HallC5×C7×C13 ⋊ C3×D11
HallC5×C7×C11 ⋊ C2×C3×C13
HallC11×ΓL(1,𝔽8) ⋊ C2×C5×C13
HallC7×D11 ⋊ C3×C5×C13
HallC11×C13 ⋊ C2×C5×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×C5×D11
HallC5×C11 ⋊ C2×C13×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×C13×D11
SylowC11 ⋊ C2×C5×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5×C13×D11

Subgroups

subgroupG/H
center, hypercenterC5×C13ΓL(1,𝔽8)×D11
commutator, cosocle, hypocenterC7×C11C2×C3×C5×C13
FrattiniC1G
Fitting, socleC5×C7×C11×C13C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C5×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5005

Conjugacy classes & character table

2275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 62);