Finite Group Databasebeta

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C3×C5×D1155 #46831669

order34650
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D1155
unambiguous semidirect productC3⋊(C3×C5×D385)
unambiguous semidirect productC5⋊(C3×C5×D231)

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derivedC3×C5×C7×C11 ⋊ C2×C3×C5
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×C5×D15
HallC32×C7 ⋊ C5×D55
SylowC52 ⋊ C3×D231
SylowC11 ⋊ C3×C5×D105
SylowC32 ⋊ C5×D385
SylowC7 ⋊ C3×C5×D165

Subgroups

subgroupG/H
center, hypercenterC3×C5D1155
commutator, cosocle, hypocenterC3×C5×C7×C11C2×C3×C5
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C3×C5

192 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 2310

Conjugacy classes & character table

8685 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 312);