Finite Group Databasebeta

← Prev (#44540764) Next (#44540766) →

C5×A4×C232 #44540765

order31740
automorphism?
homologyAbelianization (H1) = C3×C5×C232 · Schur multiplier (H2) = C2×C23

Aliases

direct productC5×A4×C232
unambiguous semidirect productC22⋊(C3×C5×C232)
unambiguous semidirect product(C22×C5)⋊(C3×C232)
unambiguous semidirect product(C22×C23)⋊(C3×C5×C23)
unambiguous semidirect product(C22×C5×C23)⋊(C3×C23)

Splittings

Fitting, socle, HallC22×C5×C232 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C232
HallC22×C232 ⋊ C3×C5
HallC22×C5 ⋊ C3×C232

Subgroups

subgroupG/H
center, hypercenterC5×C232A4
commutator, cosocle, hypocenterC22C3×C5×C232
FrattiniC1G
Fitting, socleC22×C5×C232C3
LCSG ▷ C22
UCSC1 ◁ C5×C232

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10580

Conjugacy classes & character table

10580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31740, 103);