Finite Group Databasebeta

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C5×Dic3×C17×C31 #44539255

order31620
automorphism?
homologyAbelianization (H1) = C4×C5×C17×C31 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×C17×C31
unambiguous semidirect productC3⋊(C4×C5×C17×C31)

Splittings

derived, SylowC3 ⋊ C4×C5×C17×C31
HallC3×C5×C17×C31 ⋊ C4
HallC3×C17×C31 ⋊ C4×C5
HallC3×C5×C31 ⋊ C4×C17
HallC3×C5×C17 ⋊ C4×C31
HallC3×C31 ⋊ C4×C5×C17
HallC3×C17 ⋊ C4×C5×C31
HallC3×C5 ⋊ C4×C17×C31

Subgroups

subgroupG/H
center, hypercenterC2×C5×C17×C31D3
commutator, hypocenterC3C4×C5×C17×C31
FrattiniC2C5×D3×C17×C31
Fitting, socle, prime radicalC2×C3×C5×C17×C31C2
cosocleC2×C3C2×C5×C17×C31
LCSG ▷ C3
UCSC1 ◁ C2×C5×C17×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31620

Conjugacy classes & character table

15810 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 12);