Finite Group Databasebeta

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C5×C11×#10587717 #44473275

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×#10587717

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C2×C3
derived, HallC7×C13 ⋊ C2×C3×C5×C11
HallC5×C11×#63271 ⋊ C2
HallC5×C7×C11×D13 ⋊ C3
HallC11×#63271 ⋊ C2×C5
HallC7×C11×D13 ⋊ C3×C5
HallC5×C11×D13 ⋊ ΓL(1,𝔽8)
HallC5×#63271 ⋊ C2×C11
HallC7×C11×C13 ⋊ C2×C3×C5
HallC5×C7×D13 ⋊ C3×C11
HallC5×C11×C13 ⋊ C2×ΓL(1,𝔽8)
HallC5×C7×C13 ⋊ C2×C3×C11
HallC5×C7×C11 ⋊ D13⋊C3
HallC11×D13 ⋊ C5×ΓL(1,𝔽8)
Hall#63271 ⋊ C2×C5×C11
HallC7×D13 ⋊ C3×C5×C11
HallC11×C13 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×D13 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ C5×D13⋊C3
HallC5×C13 ⋊ C2×C11×ΓL(1,𝔽8)
HallC5×C7 ⋊ C11×D13⋊C3
HallD13 ⋊ C5×C11×ΓL(1,𝔽8)
SylowC13 ⋊ C2×C5×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C5×C11×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C11#10587717
commutator, cosocle, hypocenterC7×C13C2×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C5×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5005

Conjugacy classes & character table

1320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 60);