Finite Group Databasebeta

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C3×C5×D1023 #44501877

order30690
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D1023
unambiguous semidirect productC3⋊(C3×C5×D341)

Splittings

Fitting, socle, HallC32×C5×C11×C31 ⋊ C2
derivedC3×C11×C31 ⋊ C2×C3×C5
HallC32×C11×C31 ⋊ C2×C5
HallC5×C11×C31 ⋊ C3×D3
HallC32×C5×C31 ⋊ D11
HallC32×C5×C11 ⋊ D31
HallC11×C31 ⋊ C3×C5×D3
HallC32×C31 ⋊ C5×D11
HallC5×C31 ⋊ C3×D33
HallC32×C11 ⋊ C5×D31
HallC5×C11 ⋊ C3×D93
HallC32×C5 ⋊ D341
SylowC31 ⋊ C3×C5×D33
SylowC11 ⋊ C3×C5×D93
SylowC32 ⋊ C5×D341

Subgroups

subgroupG/H
center, hypercenterC3×C5D1023
commutator, cosocle, hypocenterC3×C11×C31C2×C3×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C3×C11×C31
UCSC1 ◁ C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10230

Conjugacy classes & character table

7695 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 244);