Finite Group Databasebeta

← Prev (#36375493) Next (#36375495) →

C5×A4×C373 #36375494

order22380
automorphism?
homologyAbelianization (H1) = C3×C5×C373 · Schur multiplier (H2) = C2

Aliases

direct productC5×A4×C373
unambiguous semidirect productC22⋊(C3×C5×C373)
unambiguous semidirect product(C22×C5)⋊(C3×C373)

Splittings

Fitting, socle, HallC22×C5×C373 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C373
HallC22×C373 ⋊ C3×C5
HallC22×C5 ⋊ C3×C373

Subgroups

subgroupG/H
center, hypercenterC5×C373A4
commutator, cosocle, hypocenterC22C3×C5×C373
FrattiniC1G
Fitting, socleC22×C5×C373C3
LCSG ▷ C22
UCSC1 ◁ C5×C373

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7460

Conjugacy classes & character table

7460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22380, 43);