Finite Group Databasebeta

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C5×C7×C11×C3⋊D15 #46831678

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

Aliases

direct productC5×C7×C11×C3⋊D15
unambiguous semidirect productC3⋊(C5×C7×C11×D15)
unambiguous semidirect productC5⋊(C5×C7×C11×C3⋊D3)

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derivedC32×C5 ⋊ C2×C5×C7×C11
HallC32×C52×C11 ⋊ C2×C7
HallC52×C7×C11 ⋊ C3⋊D3
HallC32×C52×C7 ⋊ C2×C11
HallC32×C7×C11 ⋊ C5×D5
HallC52×C11 ⋊ C7×C3⋊D3
HallC32×C52 ⋊ C2×C7×C11
HallC52×C7 ⋊ C11×C3⋊D3
HallC32×C11 ⋊ C5×C7×D5
HallC32×C7 ⋊ C5×D5×C11
SylowC52 ⋊ C7×C11×C3⋊D3
SylowC32 ⋊ C5×C7×D5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C7×C11C3⋊D15
commutator, cosocle, hypocenterC32×C5C2×C5×C7×C11
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C32×C5
UCSC1 ◁ C5×C7×C11

240 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 104 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

9240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 321);