Finite Group Databasebeta

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C3×C52×D231 #46831665

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

Aliases

direct productC3×C52×D231
unambiguous semidirect productC3⋊(C3×C52×D77)

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derivedC3×C7×C11 ⋊ C2×C3×C52
HallC32×C52×C11 ⋊ D7
HallC52×C7×C11 ⋊ C3×D3
HallC32×C52×C7 ⋊ D11
HallC32×C7×C11 ⋊ C2×C52
HallC52×C11 ⋊ C3×D21
HallC32×C52 ⋊ D77
HallC52×C7 ⋊ C3×D33
HallC32×C11 ⋊ C52×D7
HallC7×C11 ⋊ C3×C52×D3
HallC32×C7 ⋊ C52×D11
SylowC11 ⋊ C3×C52×D21
SylowC32 ⋊ C52×D77
SylowC7 ⋊ C3×C52×D33

Subgroups

subgroupG/H
center, hypercenterC3×C52D231
commutator, cosocle, hypocenterC3×C7×C11C2×C3×C52
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C3×C52

288 conjugacy classes of subgroups; only the 144 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 144 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

8775 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 308);