Finite Group Databasebeta

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C5×C11×C3⋊D105 #46831680

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

Aliases

direct productC5×C11×C3⋊D105
unambiguous semidirect productC3⋊(C5×C11×D105)
unambiguous semidirect productC5⋊(C5×C11×C3⋊D21)
unambiguous semidirect productC7⋊(C5×C11×C3⋊D15)

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derivedC32×C5×C7 ⋊ C2×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 ⋊ C11×C3⋊D3
HallC32×C11 ⋊ C5×D35
HallC7×C11 ⋊ C5×C3⋊D15
HallC32×C7 ⋊ C5×D5×C11
SylowC52 ⋊ C11×C3⋊D21
SylowC32 ⋊ C5×C11×D35
SylowC7 ⋊ C5×C11×C3⋊D15

Subgroups

subgroupG/H
center, hypercenterC5×C11C3⋊D105
commutator, cosocle, hypocenterC32×C5×C7C2×C5×C11
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C32×C5×C7
UCSC1 ◁ C5×C11

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

8745 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 323);