Finite Group Databasebeta

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C5×C7×C3⋊D165 #46831679

order34650
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC5×C7×C3⋊D165
unambiguous semidirect productC3⋊(C5×C7×D165)
unambiguous semidirect productC5⋊(C5×C7×C3⋊D33)

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derivedC32×C5×C11 ⋊ C2×C5×C7
HallC32×C52×C11 ⋊ C2×C7
HallC52×C7×C11 ⋊ C3⋊D3
HallC32×C52×C7 ⋊ D11
HallC32×C7×C11 ⋊ C5×D5
HallC52×C11 ⋊ C7×C3⋊D3
HallC32×C52 ⋊ C7×D11
HallC52×C7 ⋊ C3⋊D33
HallC32×C11 ⋊ C5×C7×D5
HallC7×C11 ⋊ C5×C3⋊D15
HallC32×C7 ⋊ C5×D55
SylowC52 ⋊ C7×C3⋊D33
SylowC11 ⋊ C5×C7×C3⋊D15
SylowC32 ⋊ C5×C7×D55

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊D165
commutator, cosocle, hypocenterC32×C5×C11C2×C5×C7
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C32×C5×C11
UCSC1 ◁ C5×C7

240 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 6930

Conjugacy classes & character table

8715 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 322);