Finite Group Databasebeta

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C3×C7×C11×C3⋊(C5⋊D5) #46831670

order34650
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C5

Aliases

direct productC3×C7×C11×C3⋊(C5⋊D5)
unambiguous semidirect productC3⋊(C3×C7×C11×C5⋊D5)
unambiguous semidirect productC5⋊(C3×C7×C11×D15)

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derivedC3×C52 ⋊ C2×C3×C7×C11
HallC32×C52×C11 ⋊ C2×C7
HallC52×C7×C11 ⋊ C3×D3
HallC32×C52×C7 ⋊ C2×C11
HallC32×C7×C11 ⋊ C5⋊D5
HallC52×C11 ⋊ C3×D3×C7
HallC32×C52 ⋊ C2×C7×C11
HallC52×C7 ⋊ C3×D3×C11
HallC32×C11 ⋊ C7×C5⋊D5
HallC32×C7 ⋊ C11×C5⋊D5
SylowC52 ⋊ C3×D3×C7×C11
SylowC32 ⋊ C7×C11×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11C3⋊(C5⋊D5)
commutator, cosocle, hypocenterC3×C52C2×C3×C7×C11
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3×C52
UCSC1 ◁ C3×C7×C11

288 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 11550

Conjugacy classes & character table

9009 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 313);