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C2×C3⋊(C3⋊(C5⋊(C13⋊D13))) #44478353

order30420
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3×C13

Aliases

direct productC2×C3⋊(C3⋊(C5⋊(C13⋊D13)))
unambiguous semidirect product(C2×C3)⋊(C3⋊(C5⋊(C13⋊D13)))
unambiguous semidirect product(C2×C5)⋊(C3⋊(C3⋊(C13⋊D13)))
unambiguous semidirect product(C2×C13)⋊(C3⋊D195)

Splittings

Fitting, socleC2×C32×C5×C132 ⋊ C2
derived, HallC32×C5×C132 ⋊ C22
HallC32×C132 ⋊ C2×D5
HallC5×C132 ⋊ C2×C3⋊D3
SylowC132 ⋊ C2×C3⋊D15
HallC32×C5 ⋊ C2×C13⋊D13
SylowC32 ⋊ C2×C5⋊(C13⋊D13)
SylowC5 ⋊ C2×C3⋊(C3⋊(C13⋊D13))

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C3⋊(C5⋊(C13⋊D13)))
commutator, cosocle, hypocenterC32×C5×C132C22
FrattiniC1G
Fitting, socleC2×C32×C5×C132C2
LCSG ▷ C32×C5×C132
UCSC1 ◁ C2

960 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15210

Conjugacy classes & character table

7608 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 942);