Finite Group Databasebeta

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C2×C3×C5×C23×C13⋊C3 #41002114

order26910
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C23 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C5×C23×C13⋊C3
unambiguous semidirect product(C2×C13)⋊(C32×C5×C23)
unambiguous semidirect product(C2×C3×C13)⋊(C3×C5×C23)
unambiguous semidirect product(C2×C5×C13)⋊(C32×C23)
unambiguous semidirect product(C2×C3×C5×C13)⋊(C3×C23)
unambiguous semidirect product(C2×C13×C23)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C13×C23)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C13×C23)⋊C32
unambiguous semidirect product(C2×C3×C5×C13×C23)⋊C3

Splittings

Fitting, socleC2×C3×C5×C13×C23 ⋊ C3
derived, SylowC13 ⋊ C2×C32×C5×C23
HallC2×C5×C13×C23 ⋊ C32
HallC5×C13×C23 ⋊ C2×C32
HallC2×C13×C23 ⋊ C32×C5
HallC13×C23 ⋊ C2×C32×C5
HallC2×C5×C13 ⋊ C32×C23
HallC5×C13 ⋊ C2×C32×C23
HallC2×C13 ⋊ C32×C5×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C23C13⋊C3
commutator, cosocle, hypocenterC13C2×C32×C5×C23
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C23C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C5×C23

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8970

Conjugacy classes & character table

4830 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 41);