Finite Group Databasebeta

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C22×C17×(C31⋊C3)⋊C5 #44539300

order31620
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C17 · Schur multiplier (H2) = C2

Aliases

direct productC22×C17×(C31⋊C3)⋊C5
unambiguous semidirect product(C22×C31⋊C3)⋊(C5×C17)
unambiguous semidirect product(C22×C17×C31⋊C3)⋊C5

Splittings

Fitting, socle, HallC22×C17×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C22×C3×C5×C17
HallC22×C17×ΓL(1,𝔽32) ⋊ C3
HallC22×C17×C31⋊C3 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C22×C3
HallC17×C31⋊C3 ⋊ C22×C5
HallC22×ΓL(1,𝔽32) ⋊ C3×C17
HallC17×C31 ⋊ C22×C3×C5
HallC22×C31⋊C3 ⋊ C5×C17
HallΓL(1,𝔽32) ⋊ C22×C3×C17
HallC22×C31 ⋊ C3×C5×C17
HallC31⋊C3 ⋊ C22×C5×C17

Subgroups

subgroupG/H
center, hypercenterC22×C17(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C22×C3×C5×C17
FrattiniC1G
Fitting, socleC22×C17×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C22×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2108

Conjugacy classes & character table

1156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 57);