Finite Group Databasebeta

← Prev (#43249246) Next (#43249248) →

C2×C5⋊(D29⋊C49) #43249247

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

Aliases

direct productC2×C5⋊(D29⋊C49)
unambiguous semidirect product(C2×C5)⋊(D29⋊C49)
unambiguous semidirect product(C2×D145)⋊C49
unambiguous semidirect product(C2×C29⋊C49)⋊D5

Splittings

derived, HallC5×C29 ⋊ C22×C49
HallC5×C29⋊C49 ⋊ C22
HallC29⋊C49 ⋊ C2×D5
HallC2×D145 ⋊ C49
SylowC29 ⋊ C2×D5×C49
SylowC5 ⋊ C2×D29⋊C49

Subgroups

subgroupG/H
center, hypercenterC2×C7C5⋊(D29⋊C7)
commutator, hypocenterC5×C29C22×C49
FrattiniC7C2×C5⋊(D29⋊C7)
Fitting, socleC2×C5×C7×C29C2×C7
prime radicalC2×C7×D145C7
cosocleC5×C7×C29C22×C7
LCSG ▷ C5×C29
UCSC1 ◁ C2×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14210

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28420, 22);