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C2×C3×C13×D155 #37564003

order24180
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C13×D155
unambiguous semidirect product(C2×C5)⋊(C3×C13×D31)

Splittings

Fitting, socleC2×C3×C5×C13×C31 ⋊ C2
derived, HallC5×C31 ⋊ C22×C3×C13
HallC3×C5×C13×C31 ⋊ C22
HallC5×C13×C31 ⋊ C22×C3
HallC3×C13×C31 ⋊ C2×D5
HallC3×C5×C31 ⋊ C22×C13
HallC13×C31 ⋊ C2×C3×D5
HallC3×C5×C13 ⋊ C2×D31
HallC3×C31 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×C3×D31
SylowC31 ⋊ C2×C3×D5×C13
HallC3×C5 ⋊ C2×C13×D31
SylowC5 ⋊ C2×C3×C13×D31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D155
commutator, cosocle, hypocenterC5×C31C22×C3×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C31C2
LCSG ▷ C5×C31
UCSC1 ◁ C2×C3×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12090

Conjugacy classes & character table

6162 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 302);