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C2×C5×D29⋊C49 #43249246

order28420
automorphism?
homologyAbelianization (H1) = C22×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D29⋊C49
unambiguous semidirect productD29⋊(C2×C5×C49)
unambiguous semidirect product(C2×D29)⋊(C5×C49)
unambiguous semidirect product(C2×C5×D29)⋊C49
unambiguous semidirect product(C29⋊C49)⋊(C22×C5)
unambiguous semidirect product(C2×C29⋊C49)⋊(C2×C5)

Splittings

derived, SylowC29 ⋊ C22×C5×C49
HallC5×C29⋊C49 ⋊ C22
HallC29⋊C49 ⋊ C22×C5
HallC2×C5×D29 ⋊ C49
HallC5×C29 ⋊ C22×C49
HallC2×D29 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D29⋊C7
commutator, hypocenterC29C22×C5×C49
FrattiniC7C2×C5×D29⋊C7
Fitting, socleC2×C5×C7×C29C2×C7
prime radicalC2×C5×C7×D29C7
cosocleC7×C29C22×C5×C7
LCSG ▷ C29
UCSC1 ◁ C2×C5×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14210

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28420, 21);