Finite Group Databasebeta

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C5×C13×#3866⋊C3 #43274145

order28860
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×#3866⋊C3
unambiguous semidirect product#3866⋊(C3×C5×C13)
unambiguous semidirect product(C5×#3866)⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C13×C37 ⋊ C3×C4
derived, SylowC37 ⋊ C3×C4×C5×C13
HallC5×C13×#3866 ⋊ C3
HallC5×C13×C37⋊C3 ⋊ C4
HallC13×#3866 ⋊ C3×C5
HallC13×C37⋊C3 ⋊ C4×C5
HallC5×#3866 ⋊ C3×C13
HallC5×C37⋊C3 ⋊ C4×C13
HallC13×C37 ⋊ C3×C4×C5
HallC5×C37 ⋊ C3×C4×C13
Hall#3866 ⋊ C3×C5×C13
HallC37⋊C3 ⋊ C4×C5×C13

Subgroups

subgroupG/H
center, hypercenterC5×C13#3866⋊C3
commutator, hypocenterC37C3×C4×C5×C13
FrattiniC1G
Fitting, socleC5×C13×C37C3×C4
prime radicalC5×C13×D37⋊C3C2
cosocleD37C2×C3×C5×C13
LCSG ▷ C37
UCSC1 ◁ C5×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2405

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28860, 50);