Finite Group Databasebeta

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C2×C3×C5×D497 #44447276

order29820
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D497

Splittings

Fitting, socleC2×C3×C5×C7×C71 ⋊ C2
derived, HallC7×C71 ⋊ C22×C3×C5
HallC3×C5×C7×C71 ⋊ C22
HallC5×C7×C71 ⋊ C22×C3
HallC3×C7×C71 ⋊ C22×C5
HallC3×C5×C71 ⋊ C2×D7
HallC5×C71 ⋊ C2×C3×D7
HallC3×C71 ⋊ C2×C5×D7
HallC3×C5×C7 ⋊ C2×D71
SylowC71 ⋊ C2×C3×C5×D7
HallC5×C7 ⋊ C2×C3×D71
HallC3×C7 ⋊ C2×C5×D71
SylowC7 ⋊ C2×C3×C5×D71

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D497
commutator, cosocle, hypocenterC7×C71C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C71C2
LCSG ▷ C7×C71
UCSC1 ◁ C2×C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14910

Conjugacy classes & character table

7500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 164);