Finite Group Databasebeta

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C2×C3×C5×D511 #44501461

order30660
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D511

Splittings

Fitting, socleC2×C3×C5×C7×C73 ⋊ C2
derived, HallC7×C73 ⋊ C22×C3×C5
HallC3×C5×C7×C73 ⋊ C22
HallC5×C7×C73 ⋊ C22×C3
HallC3×C7×C73 ⋊ C22×C5
HallC3×C5×C73 ⋊ C2×D7
HallC5×C73 ⋊ C2×C3×D7
HallC3×C73 ⋊ C2×C5×D7
HallC3×C5×C7 ⋊ C2×D73
SylowC73 ⋊ C2×C3×C5×D7
HallC5×C7 ⋊ C2×C3×D73
HallC3×C7 ⋊ C2×C5×D73
SylowC7 ⋊ C2×C3×C5×D73

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D511
commutator, cosocle, hypocenterC7×C73C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C73C2
LCSG ▷ C7×C73
UCSC1 ◁ C2×C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15330

Conjugacy classes & character table

7710 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 224);