Finite Group Databasebeta

← Prev (#43242540) Next (#43242542) →

C52×C11×D51 #43242541

order28050
automorphism?
homologyAbelianization (H1) = C2×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC52×C11×D51
unambiguous semidirect productC3⋊(C52×C11×D17)
unambiguous semidirect productC17⋊(C52×D3×C11)

Splittings

Fitting, socle, HallC3×C52×C11×C17 ⋊ C2
derived, HallC3×C17 ⋊ C2×C52×C11
HallC52×C11×C17 ⋊ D3
HallC3×C52×C17 ⋊ C2×C11
HallC3×C52×C11 ⋊ D17
HallC3×C11×C17 ⋊ C2×C52
HallC52×C17 ⋊ D3×C11
HallC11×C17 ⋊ C52×D3
HallC3×C52 ⋊ C11×D17
HallC3×C11 ⋊ C52×D17
SylowC17 ⋊ C52×D3×C11
SylowC3 ⋊ C52×C11×D17

Subgroups

subgroupG/H
center, hypercenterC52×C11D51
commutator, cosocle, hypocenterC3×C17C2×C52×C11
FrattiniC1G
Fitting, socleC3×C52×C11×C17C2
LCSG ▷ C3×C17
UCSC1 ◁ C52×C11

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14025

Conjugacy classes & character table

7425 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 66);