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C5×C23×C3⋊D39 #41002132

order26910
automorphism?
homologyAbelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C3

Aliases

direct productC5×C23×C3⋊D39
unambiguous semidirect productC3⋊(C5×C23×D39)
unambiguous semidirect productC13⋊(C5×C3⋊D3×C23)

Splittings

Fitting, socle, HallC32×C5×C13×C23 ⋊ C2
derived, HallC32×C13 ⋊ C2×C5×C23
HallC32×C13×C23 ⋊ C2×C5
HallC5×C13×C23 ⋊ C3⋊D3
HallC32×C5×C23 ⋊ D13
HallC32×C5×C13 ⋊ C2×C23
HallC13×C23 ⋊ C5×C3⋊D3
HallC32×C23 ⋊ C5×D13
HallC5×C13 ⋊ C3⋊D3×C23
HallC32×C5 ⋊ C23×D13
SylowC13 ⋊ C5×C3⋊D3×C23
SylowC32 ⋊ C5×C23×D13

Subgroups

subgroupG/H
center, hypercenterC5×C23C3⋊D39
commutator, cosocle, hypocenterC32×C13C2×C5×C23
FrattiniC1G
Fitting, socleC32×C5×C13×C23C2
LCSG ▷ C32×C13
UCSC1 ◁ C5×C23

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

6900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 59);