Finite Group Databasebeta

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C32×C5×D385 #46831657

order34650
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×D385
unambiguous semidirect productC5⋊(C32×C5×D77)

Splittings

Fitting, socle, HallC32×C52×C7×C11 ⋊ C2
derivedC5×C7×C11 ⋊ C2×C32×C5
HallC32×C52×C11 ⋊ D7
HallC52×C7×C11 ⋊ C2×C32
HallC32×C52×C7 ⋊ D11
HallC32×C7×C11 ⋊ C5×D5
HallC52×C11 ⋊ C32×D7
HallC32×C52 ⋊ D77
HallC52×C7 ⋊ C32×D11
HallC32×C11 ⋊ C5×D35
HallC7×C11 ⋊ C32×C5×D5
HallC32×C7 ⋊ C5×D55
SylowC52 ⋊ C32×D77
SylowC11 ⋊ C32×C5×D35
SylowC7 ⋊ C32×C5×D55

Subgroups

subgroupG/H
center, hypercenterC32×C5D385
commutator, cosocle, hypocenterC5×C7×C11C2×C32×C5
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C5×C7×C11
UCSC1 ◁ C32×C5

240 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 108 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

8730 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 300);