Finite Group Databasebeta

← Prev (#32912464) Next (#32912466) →

C2×C5×C29×C7⋊C9 #32912465

order18270
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C29 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derived, SylowC7 ⋊ C2×C5×C9×C29
HallC2×C5×C7×C29 ⋊ C9
HallC5×C7×C29 ⋊ C2×C9
HallC2×C7×C29 ⋊ C5×C9
HallC7×C29 ⋊ C2×C5×C9
HallC2×C5×C7 ⋊ C9×C29
HallC5×C7 ⋊ C2×C9×C29
HallC2×C7 ⋊ C5×C9×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C29ΓL(1,𝔽8)
commutator, hypocenterC7C2×C5×C9×C29
FrattiniC3C2×C5×ΓL(1,𝔽8)×C29
Fitting, socle, prime radicalC2×C3×C5×C7×C29C3
cosocleC3×C7C2×C3×C5×C29
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18270

Conjugacy classes & character table

4350 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C29×C7⋊C9, C5×C7⋊C9×Dic29, C5×C29×Dic7⋊C9, …
maximal normal subgroup ofC4×C5×C29×C7⋊C9, C5×C7⋊C9×Dic29, C5×C29×Dic7⋊C9, …
maximal quotient ofC4×C5×C29×C7⋊C9, C22×C5×C29×C7⋊C9

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18270, 3);