Finite Group Databasebeta

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C5×D7×D29⋊C7 #43249299

order28420
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×D7×D29⋊C7
unambiguous semidirect productD29⋊(C5×C7×D7)
unambiguous semidirect product(D7×D29)⋊(C5×C7)
unambiguous semidirect product(C7×D29⋊C7)⋊(C2×C5)
unambiguous semidirect product(C7⋊(D29⋊C7))⋊(C2×C5)
unambiguous semidirect product(D7×C29⋊C7)⋊(C2×C5)
unambiguous semidirect product(C5×D7×D29)⋊C7

Splittings

Fitting, socleC5×C7×C29 ⋊ C22×C7
derivedC7×C29 ⋊ C22×C5×C7
HallC5×C7×C29⋊C7 ⋊ C22
HallC7×C29⋊C7 ⋊ C22×C5
HallC5×C29 ⋊ C2×C7×D7
SylowC29 ⋊ C2×C5×C7×D7

Subgroups

subgroupG/H
center, hypercenterC5D7×D29⋊C7
commutator, cosocle, hypocenterC7×C29C22×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C29C22×C7
LCSG ▷ C7×C29
UCSC1 ◁ C5

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1015

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28420, 74);