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C2×C13×D465 #37564011

order24180
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D465
unambiguous semidirect product(C2×C3)⋊(C13×D155)
unambiguous semidirect product(C2×C5)⋊(C13×D93)
unambiguous semidirect product(C2×C31)⋊(C13×D15)

Splittings

Fitting, socleC2×C3×C5×C13×C31 ⋊ C2
derived, HallC3×C5×C31 ⋊ C22×C13
HallC3×C5×C13×C31 ⋊ C22
HallC5×C13×C31 ⋊ C2×D3
HallC3×C13×C31 ⋊ C2×D5
HallC13×C31 ⋊ C2×D15
HallC3×C5×C13 ⋊ C2×D31
HallC5×C31 ⋊ C2×D3×C13
HallC3×C31 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×D93
HallC3×C13 ⋊ C2×D155
SylowC31 ⋊ C2×C13×D15
HallC3×C5 ⋊ C2×C13×D31
SylowC5 ⋊ C2×C13×D93
SylowC3 ⋊ C2×C13×D155

Subgroups

subgroupG/H
center, hypercenterC2×C13D465
commutator, cosocle, hypocenterC3×C5×C31C22×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C31C2
LCSG ▷ C3×C5×C31
UCSC1 ◁ C2×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12090

Conjugacy classes & character table

6084 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 310);