Finite Group Databasebeta

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C5×C49×C43⋊C3 #44539172

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

Aliases

direct productC5×C49×C43⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C49C43⋊C3
commutator, hypocenterC43C3×C5×C49
FrattiniC7C5×C7×C43⋊C3
FittingC5×C43×C49C3
socleC5×C7×C43C3×C7
prime radicalC5×C7×C43⋊C3C7
cosocleC7×C43C3×C5×C7
LCSG ▷ C43
UCSC1 ◁ C5×C49

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10535

Conjugacy classes & character table

4165 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31605, 3);