Finite Group Databasebeta

← Prev (#41002135) Next (#41002137) →

C23×C3⋊D195 #41002136

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

Aliases

direct productC23×C3⋊D195
unambiguous semidirect productC3⋊(C23×D195)
unambiguous semidirect productC5⋊(C23×C3⋊D39)
unambiguous semidirect productC13⋊(C23×C3⋊D15)

Splittings

Fitting, socle, HallC32×C5×C13×C23 ⋊ C2
derived, HallC32×C5×C13 ⋊ C2×C23
HallC32×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ C3⋊D3
HallC32×C5×C23 ⋊ D13
HallC13×C23 ⋊ C3⋊D15
HallC32×C23 ⋊ D65
HallC32×C13 ⋊ D5×C23
HallC5×C23 ⋊ C3⋊D39
HallC5×C13 ⋊ C3⋊D3×C23
HallC32×C5 ⋊ C23×D13
SylowC13 ⋊ C23×C3⋊D15
SylowC32 ⋊ C23×D65
SylowC5 ⋊ C23×C3⋊D39

Subgroups

subgroupG/H
center, hypercenterC23C3⋊D195
commutator, cosocle, hypocenterC32×C5×C13C2×C23
FrattiniC1G
Fitting, socleC32×C5×C13×C23C2
LCSG ▷ C32×C5×C13
UCSC1 ◁ C23

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

6762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 63);