Finite Group Databasebeta

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C3⋊D5115 #44501889

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

Aliases

unambiguous semidirect productC3⋊D5115
unambiguous semidirect productC5⋊(C3⋊D1023)
unambiguous semidirect productC11⋊(C3⋊D465)
unambiguous semidirect productC31⋊(C3⋊D165)

Splittings

Fitting, socle, derived, HallC32×C5×C11×C31 ⋊ C2
HallC32×C11×C31 ⋊ D5
HallC5×C11×C31 ⋊ C3⋊D3
HallC32×C5×C31 ⋊ D11
HallC32×C5×C11 ⋊ D31
HallC11×C31 ⋊ C3⋊D15
HallC32×C31 ⋊ D55
HallC5×C31 ⋊ C3⋊D33
HallC32×C11 ⋊ D155
HallC5×C11 ⋊ C3⋊D93
HallC32×C5 ⋊ D341
SylowC31 ⋊ C3⋊D165
SylowC11 ⋊ C3⋊D465
SylowC32 ⋊ D1705
SylowC5 ⋊ C3⋊D1023

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C11×C31C2
LCSG ▷ C32×C5×C11×C31
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Polycyclic presentation:

2,3^2,5,11,31|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^10,f^a=f^30

Conjugacy classes & character table

7674 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 256);