Finite Group Databasebeta

← Prev (#43246606) Next (#43246608) →

C5×C23×D123 #43246607

order28290
automorphism?
homologyAbelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23×D123
unambiguous semidirect productC3⋊(C5×C23×D41)

Splittings

Fitting, socle, HallC3×C5×C23×C41 ⋊ C2
derived, HallC3×C41 ⋊ C2×C5×C23
HallC5×C23×C41 ⋊ D3
HallC3×C23×C41 ⋊ C2×C5
HallC23×C41 ⋊ C5×D3
HallC3×C5×C41 ⋊ C2×C23
HallC3×C5×C23 ⋊ D41
HallC5×C41 ⋊ D3×C23
HallC3×C23 ⋊ C5×D41
SylowC41 ⋊ C5×D3×C23
HallC3×C5 ⋊ C23×D41
SylowC3 ⋊ C5×C23×D41

Subgroups

subgroupG/H
center, hypercenterC5×C23D123
commutator, cosocle, hypocenterC3×C41C2×C5×C23
FrattiniC1G
Fitting, socleC3×C5×C23×C41C2
LCSG ▷ C3×C41
UCSC1 ◁ C5×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14145

Conjugacy classes & character table

7245 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28290, 11);