Finite Group Databasebeta

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C5×D32×C7×C29 #49141594

order36540
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C29 · Schur multiplier (H2) = C2

Aliases

direct productC5×D32×C7×C29
unambiguous semidirect product(C3×D3)⋊(C2×C5×C7×C29)
unambiguous semidirect product(C3⋊D3)⋊(C2×C5×C7×C29)

Splittings

Fitting, socle, HallC32×C5×C7×C29 ⋊ C22
derived, SylowC32 ⋊ C22×C5×C7×C29
HallC32×C7×C29 ⋊ C22×C5
HallC32×C5×C29 ⋊ C22×C7
HallC32×C5×C7 ⋊ C22×C29
HallC32×C29 ⋊ C22×C5×C7
HallC32×C7 ⋊ C22×C5×C29
HallC32×C5 ⋊ C22×C7×C29

Subgroups

subgroupG/H
center, hypercenterC5×C7×C29D32
commutator, cosocle, hypocenterC32C22×C5×C7×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32
UCSC1 ◁ C5×C7×C29

176 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 6090

Conjugacy classes & character table

9135 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 436);