Finite Group Databasebeta

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C3×C5×D779 #37552571

order23370
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D779

Splittings

Fitting, socle, HallC3×C5×C19×C41 ⋊ C2
derived, HallC19×C41 ⋊ C2×C3×C5
HallC5×C19×C41 ⋊ C2×C3
HallC3×C19×C41 ⋊ C2×C5
HallC3×C5×C41 ⋊ D19
HallC3×C5×C19 ⋊ D41
HallC5×C41 ⋊ C3×D19
HallC3×C41 ⋊ C5×D19
HallC5×C19 ⋊ C3×D41
HallC3×C19 ⋊ C5×D41
SylowC41 ⋊ C3×C5×D19
SylowC19 ⋊ C3×C5×D41

Subgroups

subgroupG/H
center, hypercenterC3×C5D779
commutator, cosocle, hypocenterC19×C41C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C19×C41C2
LCSG ▷ C19×C41
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11685

Conjugacy classes & character table

5865 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23370, 7);