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C5×#15668360⋊C2 #43274161

order28860
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#15668360⋊C2
unambiguous semidirect product#15668360⋊(C2×C5)
unambiguous semidirect product#15668364⋊(C2×C5)
unambiguous semidirect product#15668368⋊(C2×C5)

Splittings

Fitting, socle, HallC5×C13×C37 ⋊ C22×C3
derived, HallC13×C37 ⋊ C22×C3×C5
HallC5×D13×D37 ⋊ C3
HallC5×#13089649 ⋊ C22
HallD13×D37 ⋊ C3×C5
Hall#13089649 ⋊ C22×C5
HallC5×C37 ⋊ C2×D13⋊C3
HallC5×C13 ⋊ C2×D37⋊C3
SylowC37 ⋊ C2×C5×D13⋊C3
SylowC13 ⋊ C2×C5×D37⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#15668360⋊C2
commutator, cosocle, hypocenterC13×C37C22×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C37C22×C3
LCSG ▷ C13×C37
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2405

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28860, 66);