Finite Group Databasebeta

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C5×C11×#63271 #28418529

order15015
isoclinismisoclinic class of #63271
automorphism?
homologyAbelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×#63271

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C3
derived, HallC7×C13 ⋊ C3×C5×C11
HallC7×C11×C13 ⋊ C3×C5
HallC5×C11×C13 ⋊ ΓL(1,𝔽8)
HallC5×C7×C13 ⋊ C3×C11
HallC5×C7×C11 ⋊ C13⋊C3
HallC11×C13 ⋊ C5×ΓL(1,𝔽8)
HallC7×C11 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C11×ΓL(1,𝔽8)
HallC5×C7 ⋊ C11×C13⋊C3
SylowC13 ⋊ C5×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C5×C11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C11#63271
commutator, cosocle, hypocenterC7×C13C3×C5×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C13C3
LCSG ▷ C7×C13
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5005

Conjugacy classes & character table

1815 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C11×#63271, C5×C11×#10587717, C5×D11×#63271, …
maximal normal subgroup ofC2×C5×C11×#63271, C5×C11×#10587717, C5×D11×#63271, …
maximal quotient ofC2×C5×C11×#63271

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15015, 6);