Finite Group Databasebeta

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C5×(C31⋊C3)⋊#595 #44539301

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

Aliases

direct productC5×(C31⋊C3)⋊#595
unambiguous semidirect product(C5×C31⋊#595)⋊C3

Splittings

Fitting, socle, HallC5×C17×C31 ⋊ C3×C4
derived, HallC17×C31 ⋊ C3×C4×C5
HallC5×C31⋊#595 ⋊ C3
HallC5×C17×C31⋊C3 ⋊ C4
HallC31⋊#595 ⋊ C3×C5
HallC17×C31⋊C3 ⋊ C4×C5
HallC5×C31⋊C3 ⋊ #595
HallC5×C31 ⋊ C3×#595
HallC31⋊C3 ⋊ C5×#595
HallC5×C17 ⋊ (C31⋊C3)⋊C4
SylowC31 ⋊ C3×C5×#595
SylowC17 ⋊ C5×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC5(C31⋊C3)⋊#595
commutator, hypocenterC17×C31C3×C4×C5
FrattiniC1G
Fitting, socleC5×C17×C31C3×C4
prime radicalC5×D17×C31⋊C3C2
cosocleC31×D17C2×C3×C5
LCSG ▷ C17×C31
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2635

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 58);