Finite Group Databasebeta

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C3×C3⋊(C5⋊D385) #46831673

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

Aliases

direct productC3×C3⋊(C5⋊D385)
unambiguous semidirect productC3⋊(C3×C5⋊D385)
unambiguous semidirect productC5⋊(C3×D1155)
unambiguous semidirect productC11⋊(C3×C3⋊(C5⋊D35))

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derivedC3×C52×C7×C11 ⋊ C2×C3
HallC32×C52×C11 ⋊ D7
HallC52×C7×C11 ⋊ C3×D3
HallC32×C52×C7 ⋊ D11
HallC32×C7×C11 ⋊ C5⋊D5
HallC52×C11 ⋊ C3×D21
HallC32×C52 ⋊ D77
HallC52×C7 ⋊ C3×D33
HallC32×C11 ⋊ C5⋊D35
HallC7×C11 ⋊ C3×C3⋊(C5⋊D5)
HallC32×C7 ⋊ C5⋊D55
SylowC52 ⋊ C3×D231
SylowC11 ⋊ C3×C3⋊(C5⋊D35)
SylowC32 ⋊ C5⋊D385
SylowC7 ⋊ C3×C3⋊(C5⋊D55)

Subgroups

subgroupG/H
center, hypercenterC3C3⋊(C5⋊D385)
commutator, cosocle, hypocenterC3×C52×C7×C11C2×C3
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3×C52×C7×C11
UCSC1 ◁ C3

288 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 130 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

8667 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 316);