Finite Group Databasebeta

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C5×Dic17×C31⋊C3 #44539271

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic17×C31⋊C3
unambiguous semidirect product(C5×C31×Dic17)⋊C3

Splittings

derived, HallC17×C31 ⋊ C3×C4×C5
HallC5×C31×Dic17 ⋊ C3
HallC5×C17×C31⋊C3 ⋊ C4
HallC5×C17×C31 ⋊ C3×C4
HallC31×Dic17 ⋊ C3×C5
HallC17×C31⋊C3 ⋊ C4×C5
HallC5×C31 ⋊ C3×Dic17
HallC5×C17 ⋊ C4×C31⋊C3
SylowC31 ⋊ C3×C5×Dic17
SylowC17 ⋊ C4×C5×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5D17×C31⋊C3
commutator, hypocenterC17×C31C3×C4×C5
FrattiniC2C5×D17×C31⋊C3
Fitting, socleC2×C5×C17×C31C2×C3
prime radicalC2×C5×C17×C31⋊C3C2
cosocleC2×C17×C31C2×C3×C5
LCSG ▷ C17×C31
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10540

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 28);