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C5×(C67⋊C3)⋊D13 #39908415

order26130
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C67⋊C3)⋊D13
unambiguous semidirect product(C67⋊C3)⋊(C5×D13)

Splittings

Fitting, socle, HallC5×C13×C67 ⋊ C2×C3
derived, HallC13×C67 ⋊ C2×C3×C5
HallC5×C13×C67⋊C3 ⋊ C2
HallC5×D871 ⋊ C3
HallC13×C67⋊C3 ⋊ C2×C5
HallD871 ⋊ C3×C5
HallC5×C67⋊C3 ⋊ D13
HallC5×C67 ⋊ C3×D13
HallC67⋊C3 ⋊ C5×D13
SylowC67 ⋊ C3×C5×D13
HallC5×C13 ⋊ D67⋊C3
SylowC13 ⋊ C5×D67⋊C3

Subgroups

subgroupG/H
center, hypercenterC5(C67⋊C3)⋊D13
commutator, cosocle, hypocenterC13×C67C2×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C67C2×C3
LCSG ▷ C13×C67
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4355

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26130, 29);