Finite Group Databasebeta

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C3×C5×C11×D105 #46831668

order34650
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C11×D105
unambiguous semidirect productC3⋊(C3×C5×C11×D35)
unambiguous semidirect productC5⋊(C3×C5×C11×D21)

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derivedC3×C5×C7 ⋊ C2×C3×C5×C11
HallC32×C52×C11 ⋊ D7
HallC52×C7×C11 ⋊ C3×D3
HallC32×C52×C7 ⋊ C2×C11
HallC32×C7×C11 ⋊ C5×D5
HallC52×C11 ⋊ C3×D21
HallC32×C52 ⋊ C11×D7
HallC52×C7 ⋊ C3×D3×C11
HallC32×C11 ⋊ C5×D35
HallC7×C11 ⋊ C3×C5×D15
HallC32×C7 ⋊ C5×D5×C11
SylowC52 ⋊ C3×C11×D21
SylowC32 ⋊ C5×C11×D35
SylowC7 ⋊ C3×C5×C11×D15

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11D105
commutator, cosocle, hypocenterC3×C5×C7C2×C3×C5×C11
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C3×C5×C11

192 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 72 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

8910 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 311);