Finite Group Databasebeta

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C5×D2289 #37504331

order22890
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2289
unambiguous semidirect productC3⋊(C5×D763)
unambiguous semidirect productC7⋊(C5×D327)
unambiguous semidirect productC109⋊(C5×D21)

Splittings

Fitting, socle, HallC3×C5×C7×C109 ⋊ C2
derived, HallC3×C7×C109 ⋊ C2×C5
HallC5×C7×C109 ⋊ D3
HallC3×C5×C109 ⋊ D7
HallC7×C109 ⋊ C5×D3
HallC5×C109 ⋊ D21
HallC3×C109 ⋊ C5×D7
SylowC109 ⋊ C5×D21
HallC3×C5×C7 ⋊ D109
HallC5×C7 ⋊ D327
HallC3×C7 ⋊ C5×D109
HallC3×C5 ⋊ D763
SylowC7 ⋊ C5×D327
SylowC3 ⋊ C5×D763

Subgroups

subgroupG/H
center, hypercenterC5D2289
commutator, cosocle, hypocenterC3×C7×C109C2×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C109C2
LCSG ▷ C3×C7×C109
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11445

Conjugacy classes & character table

5730 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22890, 16);