Finite Group Databasebeta

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C5×C3⋊(C5⋊(D67⋊C3)) #44474684

order30150
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(C5⋊(D67⋊C3))
unambiguous semidirect productC3⋊(C5×C5⋊(D67⋊C3))
unambiguous semidirect productC5⋊(C5×C3⋊(D67⋊C3))
unambiguous semidirect product(C67⋊C3)⋊(C5×D15)
unambiguous semidirect productD1005⋊(C3×C5)
unambiguous semidirect product(C5×D1005)⋊C3

Splittings

Fitting, socleC3×C52×C67 ⋊ C2×C3
derivedC3×C5×C67 ⋊ C2×C3×C5
HallC3×C52×C67⋊C3 ⋊ C2
HallC52×C67 ⋊ C3×D3
HallC3×C67⋊C3 ⋊ C5×D5
SylowC67 ⋊ C3×C5×D15
SylowC52 ⋊ C3⋊(D67⋊C3)

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C5⋊(D67⋊C3))
commutator, cosocle, hypocenterC3×C5×C67C2×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C67C2×C3
LCSG ▷ C3×C5×C67
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2010

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30150, 93);