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C2×C5×C9×C29⋊C7 #32912464

order18270
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C9×C29⋊C7
unambiguous semidirect product(C2×C29)⋊(C5×C7×C9)
unambiguous semidirect product(C2×C5×C29)⋊(C7×C9)
unambiguous semidirect product(C2×C9×C29)⋊(C5×C7)
unambiguous semidirect product(C2×C5×C9×C29)⋊C7

Splittings

Fitting, HallC2×C5×C9×C29 ⋊ C7
derived, SylowC29 ⋊ C2×C5×C7×C9
HallC5×C9×C29 ⋊ C2×C7
HallC2×C9×C29 ⋊ C5×C7
HallC2×C5×C29 ⋊ C7×C9
HallC9×C29 ⋊ C2×C5×C7
HallC5×C29 ⋊ C2×C7×C9
HallC2×C29 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9C29⋊C7
commutator, hypocenterC29C2×C5×C7×C9
FrattiniC3C2×C3×C5×C29⋊C7
FittingC2×C5×C9×C29C7
socleC2×C3×C5×C29C3×C7
prime radicalC2×C3×C5×C29⋊C7C3
cosocleC3×C29C2×C3×C5×C7
LCSG ▷ C29
UCSC1 ◁ C2×C5×C9

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2610

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC4×C5×C9×C29⋊C7, C5×C9×Dic29⋊C7, C9×Dic5×C29⋊C7, …
maximal normal subgroup ofC4×C5×C9×C29⋊C7, C5×C9×Dic29⋊C7, C9×Dic5×C29⋊C7, …
maximal quotient ofC4×C5×C9×C29⋊C7, C22×C5×C9×C29⋊C7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 2);