Finite Group Databasebeta

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C2×C49×C71⋊C5 #46852322

order34790
automorphism?
homologyAbelianization (H1) = C2×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC2×C49×C71⋊C5
unambiguous semidirect product(C2×C49×C71)⋊C5

Splittings

Fitting, HallC2×C49×C71 ⋊ C5
derived, SylowC71 ⋊ C2×C5×C49
HallC49×C71 ⋊ C2×C5
HallC2×C71 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC2×C49C71⋊C5
commutator, hypocenterC71C2×C5×C49
FrattiniC7C2×C7×C71⋊C5
FittingC2×C49×C71C5
socleC2×C7×C71C5×C7
prime radicalC2×C7×C71⋊C5C7
cosocleC7×C71C2×C5×C7
LCSG ▷ C71
UCSC1 ◁ C2×C49

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6958

Conjugacy classes & character table

1862 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34790, 3);