Finite Group Databasebeta

← Prev (#44477105) Next (#44477107) →

C2×C49×D31⋊C5 #44477106

order30380
automorphism?
homologyAbelianization (H1) = C22×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C49×D31⋊C5
unambiguous semidirect productD31⋊(C2×C5×C49)
unambiguous semidirect product(C2×D31)⋊(C5×C49)
unambiguous semidirect productΓL(1,𝔽32)⋊(C22×C49)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C2×C49)
unambiguous semidirect product(C2×C49×D31)⋊C5

Splittings

FittingC2×C31×C49 ⋊ C2×C5
derived, SylowC31 ⋊ C22×C5×C49
HallC49×ΓL(1,𝔽32) ⋊ C22
HallC2×C49×D31 ⋊ C5
HallC31×C49 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C22×C49
HallC2×D31 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC2×C49D31⋊C5
commutator, hypocenterC31C22×C5×C49
FrattiniC7C2×C7×D31⋊C5
FittingC2×C31×C49C2×C5
socleC2×C7×C31C2×C5×C7
prime radicalC2×C7×D31⋊C5C7
cosocleC7×C31C22×C5×C7
LCSG ▷ C31
UCSC1 ◁ C2×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3038

Conjugacy classes & character table

1274 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 15);