Finite Group Databasebeta

← Prev (#41002127) Next (#41002129) →

C3×C23×D195 #41002128

order26910
automorphism?
homologyAbelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×D195
unambiguous semidirect productC3⋊(C3×C23×D65)
unambiguous semidirect productC5⋊(C3×C23×D39)

Splittings

Fitting, socle, HallC32×C5×C13×C23 ⋊ C2
derivedC3×C5×C13 ⋊ C2×C3×C23
HallC32×C13×C23 ⋊ D5
HallC5×C13×C23 ⋊ C3×D3
HallC32×C5×C23 ⋊ D13
HallC32×C5×C13 ⋊ C2×C23
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 ⋊ C3×C23×D15
SylowC32 ⋊ C23×D65
SylowC5 ⋊ C3×C23×D39

Subgroups

subgroupG/H
center, hypercenterC3×C23D195
commutator, cosocle, hypocenterC3×C5×C13C2×C3×C23
FrattiniC1G
Fitting, socleC32×C5×C13×C23C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C3×C23

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8970

Conjugacy classes & character table

6831 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 55);