Finite Group Databasebeta

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C52×D561 #43242543

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

Aliases

direct productC52×D561
unambiguous semidirect productC3⋊(C52×D187)
unambiguous semidirect productC17⋊(C52×D33)

Splittings

Fitting, socle, HallC3×C52×C11×C17 ⋊ C2
derived, HallC3×C11×C17 ⋊ C2×C52
HallC52×C11×C17 ⋊ D3
HallC3×C52×C17 ⋊ D11
HallC3×C52×C11 ⋊ D17
HallC52×C17 ⋊ D33
HallC52×C11 ⋊ D51
HallC11×C17 ⋊ C52×D3
HallC3×C52 ⋊ D187
HallC3×C17 ⋊ C52×D11
HallC3×C11 ⋊ C52×D17
SylowC17 ⋊ C52×D33
SylowC11 ⋊ C52×D51
SylowC3 ⋊ C52×D187

Subgroups

subgroupG/H
center, hypercenterC52D561
commutator, cosocle, hypocenterC3×C11×C17C2×C52
FrattiniC1G
Fitting, socleC3×C52×C11×C17C2
LCSG ▷ C3×C11×C17
UCSC1 ◁ C52

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14025

Conjugacy classes & character table

7050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 68);