Finite Group Databasebeta

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C2×C5×C7×D247 #46829188

order34580
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D247
unambiguous semidirect product(C2×C13)⋊(C5×C7×D19)
unambiguous semidirect product(C2×C19)⋊(C5×C7×D13)

Splittings

Fitting, socleC2×C5×C7×C13×C19 ⋊ C2
derived, HallC13×C19 ⋊ C22×C5×C7
HallC5×C7×C13×C19 ⋊ C22
HallC7×C13×C19 ⋊ C22×C5
HallC5×C13×C19 ⋊ C22×C7
HallC5×C7×C19 ⋊ C2×D13
HallC5×C7×C13 ⋊ C2×D19
HallC7×C19 ⋊ C2×C5×D13
HallC5×C19 ⋊ C2×C7×D13
HallC7×C13 ⋊ C2×C5×D19
HallC5×C13 ⋊ C2×C7×D19
SylowC19 ⋊ C2×C5×C7×D13
SylowC13 ⋊ C2×C5×C7×D19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D247
commutator, cosocle, hypocenterC13×C19C22×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C13×C19C2
LCSG ▷ C13×C19
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17290

Conjugacy classes & character table

8750 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34580, 79);