Finite Group Databasebeta

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C3×C5×C31×#595 #44539335

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C31×#595

Splittings

Fitting, socle, HallC3×C5×C17×C31 ⋊ C4
derived, SylowC17 ⋊ C3×C4×C5×C31
HallC5×C17×C31 ⋊ C3×C4
HallC3×C17×C31 ⋊ C4×C5
HallC17×C31 ⋊ C3×C4×C5
HallC3×C5×C17 ⋊ C4×C31
HallC5×C17 ⋊ C3×C4×C31
HallC3×C17 ⋊ C4×C5×C31

Subgroups

subgroupG/H
center, hypercenterC3×C5×C31#595
commutator, hypocenterC17C3×C4×C5×C31
FrattiniC1G
Fitting, socleC3×C5×C17×C31C4
prime radicalC3×C5×C31×D17C2
cosocleD17C2×C3×C5×C31
LCSG ▷ C17
UCSC1 ◁ C3×C5×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7905

Conjugacy classes & character table

3720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 92);