Finite Group Databasebeta

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C5×C7×D109⋊C3 #37504336

order22890
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×D109⋊C3
unambiguous semidirect productD109⋊(C3×C5×C7)
unambiguous semidirect product(C109⋊C3)⋊(C2×C5×C7)
unambiguous semidirect product(C5×D109)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C109 ⋊ C2×C3
derived, SylowC109 ⋊ C2×C3×C5×C7
HallC5×C7×C109⋊C3 ⋊ C2
HallC5×C7×D109 ⋊ C3
HallC7×C109⋊C3 ⋊ C2×C5
HallC5×C109⋊C3 ⋊ C2×C7
HallC7×D109 ⋊ C3×C5
HallC5×D109 ⋊ C3×C7
HallC7×C109 ⋊ C2×C3×C5
HallC5×C109 ⋊ C2×C3×C7
HallC109⋊C3 ⋊ C2×C5×C7
HallD109 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC5×C7D109⋊C3
commutator, cosocle, hypocenterC109C2×C3×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C109C2×C3
LCSG ▷ C109
UCSC1 ◁ C5×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3815

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22890, 21);