Finite Group Databasebeta

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C32×D1705 #44501873

order30690
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC32×D1705
unambiguous semidirect productC5⋊(C32×D341)
unambiguous semidirect productC11⋊(C32×D155)

Splittings

Fitting, socle, HallC32×C5×C11×C31 ⋊ C2
derived, HallC5×C11×C31 ⋊ C2×C32
HallC32×C11×C31 ⋊ D5
HallC32×C5×C31 ⋊ D11
HallC32×C5×C11 ⋊ D31
HallC11×C31 ⋊ C32×D5
HallC32×C31 ⋊ D55
HallC5×C31 ⋊ C32×D11
HallC32×C11 ⋊ D155
HallC5×C11 ⋊ C32×D31
HallC32×C5 ⋊ D341
SylowC31 ⋊ C32×D55
SylowC11 ⋊ C32×D155
SylowC5 ⋊ C32×D341

Subgroups

subgroupG/H
center, hypercenterC32D1705
commutator, cosocle, hypocenterC5×C11×C31C2×C32
FrattiniC1G
Fitting, socleC32×C5×C11×C31C2
LCSG ▷ C5×C11×C31
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

7686 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 240);