Finite Group Databasebeta

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C5×C17×(C31⋊C3)⋊C4 #44539270

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×(C31⋊C3)⋊C4
unambiguous semidirect product(C5×Dic31)⋊(C3×C17)
unambiguous semidirect product(C5×C17×Dic31)⋊C3

Splittings

derived, SylowC31 ⋊ C3×C4×C5×C17
HallC5×C17×Dic31 ⋊ C3
HallC5×C17×C31⋊C3 ⋊ C4
HallC5×C17×C31 ⋊ C3×C4
HallC17×Dic31 ⋊ C3×C5
HallC17×C31⋊C3 ⋊ C4×C5
HallC5×Dic31 ⋊ C3×C17
HallC17×C31 ⋊ C3×C4×C5
HallC5×C31⋊C3 ⋊ C4×C17
HallC5×C31 ⋊ C3×C4×C17
HallDic31 ⋊ C3×C5×C17
HallC31⋊C3 ⋊ C4×C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17D31⋊C3
commutator, hypocenterC31C3×C4×C5×C17
FrattiniC2C5×C17×D31⋊C3
Fitting, socleC2×C5×C17×C31C2×C3
prime radicalC2×C5×C17×C31⋊C3C2
cosocleC2×C31C2×C3×C5×C17
LCSG ▷ C31
UCSC1 ◁ C2×C5×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10540

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 27);