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C2×C13×D15×C31 #37564010

order24180
automorphism?
homologyAbelianization (H1) = C22×C13×C31 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D15×C31
unambiguous semidirect product(C2×C3)⋊(D5×C13×C31)
unambiguous semidirect product(C2×C5)⋊(D3×C13×C31)

Splittings

Fitting, socleC2×C3×C5×C13×C31 ⋊ C2
derived, HallC3×C5 ⋊ C22×C13×C31
HallC3×C5×C13×C31 ⋊ C22
HallC5×C13×C31 ⋊ C2×D3
HallC3×C13×C31 ⋊ C2×D5
HallC3×C5×C31 ⋊ C22×C13
HallC3×C5×C13 ⋊ C22×C31
HallC5×C31 ⋊ C2×D3×C13
HallC3×C31 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×D3×C31
HallC3×C13 ⋊ C2×D5×C31
SylowC5 ⋊ C2×D3×C13×C31
SylowC3 ⋊ C2×D5×C13×C31

Subgroups

subgroupG/H
center, hypercenterC2×C13×C31D15
commutator, cosocle, hypocenterC3×C5C22×C13×C31
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C31C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C13×C31

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12090

Conjugacy classes & character table

7254 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 309);