Finite Group Databasebeta

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C7×D5×D29⋊C7 #43249309

order28420
automorphism?
homologyAbelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC7×D5×D29⋊C7
unambiguous semidirect productD29⋊(C72×D5)
unambiguous semidirect product(D5×D29)⋊C72
unambiguous semidirect product(C5×D29⋊C7)⋊(C2×C7)
unambiguous semidirect product(D5×C29⋊C7)⋊(C2×C7)
unambiguous semidirect product(C5⋊(D29⋊C7))⋊(C2×C7)
unambiguous semidirect product(C7×D5×D29)⋊C7

Splittings

Fitting, socleC5×C7×C29 ⋊ C22×C7
derived, HallC5×C29 ⋊ C22×C72
HallC5×C7×C29⋊C7 ⋊ C22
HallC7×C29⋊C7 ⋊ C2×D5
HallD5×D29 ⋊ C72
SylowC29 ⋊ C2×C72×D5
SylowC5 ⋊ C2×C7×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC7D5×D29⋊C7
commutator, cosocle, hypocenterC5×C29C22×C72
FrattiniC1G
Fitting, socleC5×C7×C29C22×C7
LCSG ▷ C5×C29
UCSC1 ◁ C7

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1015

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28420, 84);