Finite Group Databasebeta

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C4×C5×C7×C29⋊C7 #43249284

order28420
automorphism?
homologyAbelianization (H1) = C4×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC4×C5×C7×C29⋊C7
unambiguous semidirect product(C4×C29)⋊(C5×C72)
unambiguous semidirect product(C4×C5×C29)⋊C72
unambiguous semidirect product(C4×C7×C29)⋊(C5×C7)
unambiguous semidirect product(C4×C5×C7×C29)⋊C7

Splittings

FittingC4×C5×C7×C29 ⋊ C7
derived, SylowC29 ⋊ C4×C5×C72
HallC4×C5×C29 ⋊ C72
HallC5×C29 ⋊ C4×C72
HallC4×C29 ⋊ C5×C72

Subgroups

subgroupG/H
center, hypercenterC4×C5×C7C29⋊C7
commutator, hypocenterC29C4×C5×C72
FrattiniC2C2×C5×C7×C29⋊C7
FittingC4×C5×C7×C29C7
socleC2×C5×C7×C29C2×C7
prime radicalC2×C5×C7×C29⋊C7C2
cosocleC2×C29C2×C5×C72
LCSG ▷ C29
UCSC1 ◁ C4×C5×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4060

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28420, 59);