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C2×C3×C7×D5×C73 #44501462

order30660
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C73 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D5×C73
unambiguous semidirect productC5⋊(C22×C3×C7×C73)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C7×C73)

Splittings

Fitting, socleC2×C3×C5×C7×C73 ⋊ C2
derived, SylowC5 ⋊ C22×C3×C7×C73
HallC3×C5×C7×C73 ⋊ C22
HallC5×C7×C73 ⋊ C22×C3
HallC3×C5×C73 ⋊ C22×C7
HallC5×C73 ⋊ C22×C3×C7
HallC3×C5×C7 ⋊ C22×C73
HallC5×C7 ⋊ C22×C3×C73
HallC3×C5 ⋊ C22×C7×C73

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C73D5
commutator, cosocle, hypocenterC5C22×C3×C7×C73
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C73C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C7×C73

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15330

Conjugacy classes & character table

12264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 225);