Finite Group Databasebeta

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C2×C5×C17×D93 #44539405

order31620
automorphism?
homologyAbelianization (H1) = C22×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C17×D93
unambiguous semidirect product(C2×C3)⋊(C5×C17×D31)

Splittings

Fitting, socleC2×C3×C5×C17×C31 ⋊ C2
derived, HallC3×C31 ⋊ C22×C5×C17
HallC3×C5×C17×C31 ⋊ C22
HallC5×C17×C31 ⋊ C2×D3
HallC3×C17×C31 ⋊ C22×C5
HallC17×C31 ⋊ C2×C5×D3
HallC3×C5×C31 ⋊ C22×C17
HallC3×C5×C17 ⋊ C2×D31
HallC5×C31 ⋊ C2×D3×C17
HallC3×C17 ⋊ C2×C5×D31
SylowC31 ⋊ C2×C5×D3×C17
HallC3×C5 ⋊ C2×C17×D31
SylowC3 ⋊ C2×C5×C17×D31

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17D93
commutator, cosocle, hypocenterC3×C31C22×C5×C17
FrattiniC1G
Fitting, socleC2×C3×C5×C17×C31C2
LCSG ▷ C3×C31
UCSC1 ◁ C2×C5×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15810

Conjugacy classes & character table

8160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 162);