Finite Group Databasebeta

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C7×C25×C29⋊C7 #48001002

order35525
automorphism?
homologyAbelianization (H1) = C72×C25 · Schur multiplier (H2) = C7

Aliases

direct productC7×C25×C29⋊C7
unambiguous semidirect productC29⋊(C72×C25)
unambiguous semidirect product(C7×C29)⋊(C7×C25)
unambiguous semidirect product(C25×C29)⋊C72
unambiguous semidirect product(C7×C25×C29)⋊C7

Splittings

FittingC7×C25×C29 ⋊ C7
derived, SylowC29 ⋊ C72×C25
HallC25×C29 ⋊ C72

Subgroups

subgroupG/H
center, hypercenterC7×C25C29⋊C7
commutator, hypocenterC29C72×C25
FrattiniC5C5×C7×C29⋊C7
FittingC7×C25×C29C7
socleC5×C7×C29C5×C7
prime radicalC5×C7×C29⋊C7C5
cosocleC5×C29C5×C72
LCSG ▷ C29
UCSC1 ◁ C7×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5075

Conjugacy classes & character table

1925 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35525, 6);