Finite Group Databasebeta

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C5×(C43⋊C3)⋊C49 #44539176

order31605
automorphism?
homologyAbelianization (H1) = C3×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C43⋊C3)⋊C49
unambiguous semidirect product(C43⋊C3)⋊(C5×C49)
unambiguous semidirect product(C5×C43⋊C3)⋊C49
unambiguous semidirect product(C43⋊C49)⋊(C3×C5)
unambiguous semidirect product(C5×C43⋊C49)⋊C3

Splittings

derived, SylowC43 ⋊ C3×C5×C49
HallC5×C43⋊C49 ⋊ C3
HallC43⋊C49 ⋊ C3×C5
HallC5×C43⋊C3 ⋊ C49
HallC5×C43 ⋊ C3×C49
HallC43⋊C3 ⋊ C5×C49

Subgroups

subgroupG/H
center, hypercenterC5×C7(C43⋊C3)⋊C7
commutator, hypocenterC43C3×C5×C49
FrattiniC7C5×(C43⋊C3)⋊C7
Fitting, socleC5×C7×C43C3×C7
prime radicalC5×C7×C43⋊C3C7
cosocleC7×C43C3×C5×C7
LCSG ▷ C43
UCSC1 ◁ C5×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10535

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31605, 7);