Finite Group Databasebeta

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C2×C3×C5×C7×D85 #49088044

order35700
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C7×D85
unambiguous semidirect product(C2×C5)⋊(C3×C5×C7×D17)
unambiguous semidirect product(C2×C17)⋊(C3×C5×C7×D5)

Splittings

Fitting, socleC2×C3×C52×C7×C17 ⋊ C2
derivedC5×C17 ⋊ C22×C3×C5×C7
HallC3×C52×C7×C17 ⋊ C22
HallC52×C7×C17 ⋊ C22×C3
HallC3×C52×C17 ⋊ C22×C7
HallC3×C52×C7 ⋊ C2×D17
HallC52×C17 ⋊ C22×C3×C7
HallC3×C7×C17 ⋊ C2×C5×D5
HallC52×C7 ⋊ C2×C3×D17
HallC7×C17 ⋊ C2×C3×C5×D5
HallC3×C52 ⋊ C2×C7×D17
HallC3×C17 ⋊ C2×C5×C7×D5
SylowC52 ⋊ C2×C3×C7×D17
SylowC17 ⋊ C2×C3×C5×C7×D5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7D85
commutator, cosocle, hypocenterC5×C17C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C17C2
LCSG ▷ C5×C17
UCSC1 ◁ C2×C3×C5×C7

192 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7140

Conjugacy classes & character table

9240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 518);