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C5×C7×C22⋊(C73⋊C3) #44501451

order30660
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×C22⋊(C73⋊C3)
unambiguous semidirect productC22⋊(C5×C7×C73⋊C3)
unambiguous semidirect product(C22×C5)⋊(C7×C73⋊C3)
unambiguous semidirect productC73⋊(C5×C7×A4)
unambiguous semidirect product(C5×C73)⋊(C7×A4)

Splittings

Fitting, socle, HallC22×C5×C7×C73 ⋊ C3
derived, HallC22×C73 ⋊ C3×C5×C7
HallC5×C7×C73 ⋊ A4
HallC22×C7×C73 ⋊ C3×C5
HallC22×C5×C73 ⋊ C3×C7
HallC7×C73 ⋊ C5×A4
HallC5×C73 ⋊ C7×A4
HallC22×C5×C7 ⋊ C73⋊C3
SylowC73 ⋊ C5×C7×A4
HallC22×C7 ⋊ C5×C73⋊C3
HallC22×C5 ⋊ C7×C73⋊C3
SylowC22 ⋊ C5×C7×C73⋊C3

Subgroups

subgroupG/H
center, hypercenterC5×C7C22⋊(C73⋊C3)
commutator, cosocle, hypocenterC22×C73C3×C5×C7
FrattiniC1G
Fitting, socleC22×C5×C7×C73C3
LCSG ▷ C22×C73
UCSC1 ◁ C5×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10220

Conjugacy classes & character table

3500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 214);