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C109×D105 #37504334

order22890
automorphism?
homologyAbelianization (H1) = C2×C109 · Schur multiplier (H2) = C1

Aliases

direct productC109×D105
unambiguous semidirect productC3⋊(D35×C109)
unambiguous semidirect productC5⋊(D21×C109)
unambiguous semidirect productC7⋊(D15×C109)

Splittings

Fitting, socle, HallC3×C5×C7×C109 ⋊ C2
derived, HallC3×C5×C7 ⋊ C2×C109
HallC5×C7×C109 ⋊ D3
HallC3×C7×C109 ⋊ D5
HallC3×C5×C109 ⋊ D7
HallC7×C109 ⋊ D15
HallC5×C109 ⋊ D21
HallC3×C109 ⋊ D35
HallC5×C7 ⋊ D3×C109
HallC3×C7 ⋊ D5×C109
HallC3×C5 ⋊ D7×C109
SylowC7 ⋊ D15×C109
SylowC5 ⋊ D21×C109
SylowC3 ⋊ D35×C109

Subgroups

subgroupG/H
center, hypercenterC109D105
commutator, cosocle, hypocenterC3×C5×C7C2×C109
FrattiniC1G
Fitting, socleC3×C5×C7×C109C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C109

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11445

Conjugacy classes & character table

5886 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22890, 19);