Finite Group Databasebeta

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C3×C52×D3×C7×C11 #46831662

order34650
automorphism?
homologyAbelianization (H1) = C2×C3×C52×C7×C11 · Schur multiplier (H2) = C5

Aliases

direct productC3×C52×D3×C7×C11
unambiguous semidirect productC3⋊(C2×C3×C52×C7×C11)

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derivedC3 ⋊ C2×C3×C52×C7×C11
HallC32×C52×C11 ⋊ C2×C7
HallC32×C52×C7 ⋊ C2×C11
HallC32×C7×C11 ⋊ C2×C52
HallC32×C52 ⋊ C2×C7×C11
HallC32×C11 ⋊ C2×C52×C7
HallC32×C7 ⋊ C2×C52×C11
SylowC32 ⋊ C2×C52×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C52×C7×C11D3
commutator, cosocle, hypocenterC3C2×C3×C52×C7×C11
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3
UCSC1 ◁ C3×C52×C7×C11

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

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 192 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

17325 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 305);