Finite Group Databasebeta

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C2×C7×D251⋊C5 #47975754

order35140
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D251⋊C5
unambiguous semidirect productD251⋊(C2×C5×C7)
unambiguous semidirect product(C2×D251)⋊(C5×C7)
unambiguous semidirect product(C251⋊C5)⋊(C22×C7)
unambiguous semidirect product(C2×C251⋊C5)⋊(C2×C7)
unambiguous semidirect product(C2×C7×D251)⋊C5

Splittings

Fitting, socleC2×C7×C251 ⋊ C2×C5
derived, SylowC251 ⋊ C22×C5×C7
HallC7×C251⋊C5 ⋊ C22
HallC2×C7×D251 ⋊ C5
HallC7×C251 ⋊ C22×C5
HallC251⋊C5 ⋊ C22×C7
HallC2×D251 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7D251⋊C5
commutator, cosocle, hypocenterC251C22×C5×C7
FrattiniC1G
Fitting, socleC2×C7×C251C2×C5
LCSG ▷ C251
UCSC1 ◁ C2×C7

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3514

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35140, 15);