Finite Group Databasebeta

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C5×D2805 #43242547

order28050
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D2805
unambiguous semidirect productC3⋊(C5×D935)
unambiguous semidirect productC5⋊(C5×D561)
unambiguous semidirect productC17⋊(C5×D165)

Splittings

Fitting, socle, HallC3×C52×C11×C17 ⋊ C2
derivedC3×C5×C11×C17 ⋊ C2×C5
HallC52×C11×C17 ⋊ D3
HallC3×C52×C17 ⋊ D11
HallC3×C52×C11 ⋊ D17
HallC3×C11×C17 ⋊ C5×D5
HallC52×C17 ⋊ D33
HallC52×C11 ⋊ D51
HallC11×C17 ⋊ C5×D15
HallC3×C52 ⋊ D187
HallC3×C17 ⋊ C5×D55
HallC3×C11 ⋊ C5×D85
SylowC52 ⋊ D561
SylowC17 ⋊ C5×D165
SylowC11 ⋊ C5×D255
SylowC3 ⋊ C5×D935

Subgroups

subgroupG/H
center, hypercenterC5D2805
commutator, cosocle, hypocenterC3×C5×C11×C17C2×C5
FrattiniC1G
Fitting, socleC3×C52×C11×C17C2
LCSG ▷ C3×C5×C11×C17
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5610

Conjugacy classes & character table

7020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28050, 72);