Finite Group Databasebeta

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C2×C52×C7×D51 #49088052

order35700
automorphism?
homologyAbelianization (H1) = C22×C52×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×C7×D51
unambiguous semidirect product(C2×C3)⋊(C52×C7×D17)
unambiguous semidirect product(C2×C17)⋊(C52×D3×C7)

Splittings

Fitting, socleC2×C3×C52×C7×C17 ⋊ C2
derived, HallC3×C17 ⋊ C22×C52×C7
HallC3×C52×C7×C17 ⋊ C22
HallC52×C7×C17 ⋊ C2×D3
HallC3×C52×C17 ⋊ C22×C7
HallC3×C52×C7 ⋊ C2×D17
HallC52×C17 ⋊ C2×D3×C7
HallC3×C7×C17 ⋊ C22×C52
HallC7×C17 ⋊ C2×C52×D3
HallC3×C52 ⋊ C2×C7×D17
HallC3×C7 ⋊ C2×C52×D17
SylowC17 ⋊ C2×C52×D3×C7
SylowC3 ⋊ C2×C52×C7×D17

Subgroups

subgroupG/H
center, hypercenterC2×C52×C7D51
commutator, cosocle, hypocenterC3×C17C22×C52×C7
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C17C2
LCSG ▷ C3×C17
UCSC1 ◁ C2×C52×C7

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17850

Conjugacy classes & character table

9450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 526);