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C5×C13×(C31⋊C3)⋊C5 #44475229

order30225
automorphism?
homologyAbelianization (H1) = C3×C52×C13 · Schur multiplier (H2) = C5

Aliases

direct productC5×C13×(C31⋊C3)⋊C5
unambiguous semidirect product(C31⋊C3)⋊(C52×C13)
unambiguous semidirect productΓL(1,𝔽32)⋊(C3×C5×C13)
unambiguous semidirect product(C5×C31⋊C3)⋊(C5×C13)
unambiguous semidirect product(C5×ΓL(1,𝔽32))⋊(C3×C13)
unambiguous semidirect product(C13×C31⋊C3)⋊C52
unambiguous semidirect product(C5×C13×C31⋊C3)⋊C5

Splittings

Fitting, socleC5×C13×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C3×C52×C13
HallC5×C13×ΓL(1,𝔽32) ⋊ C3
HallC13×C31⋊C3 ⋊ C52
HallC5×ΓL(1,𝔽32) ⋊ C3×C13
HallC13×C31 ⋊ C3×C52
HallC31⋊C3 ⋊ C52×C13

Subgroups

subgroupG/H
center, hypercenterC5×C13(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C3×C52×C13
FrattiniC1G
Fitting, socleC5×C13×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C5×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2015

Conjugacy classes & character table

1105 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30225, 12);