Finite Group Databasebeta

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C2×C5×C47×C7⋊C9 #44444065

order29610
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C47 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C47×C7⋊C9
unambiguous semidirect product(C2×C7)⋊(C5×C9×C47)
unambiguous semidirect product(C2×C5×C7)⋊(C9×C47)
unambiguous semidirect product(C2×C7×C47)⋊(C5×C9)
unambiguous semidirect product(C2×C5×C7×C47)⋊C9

Splittings

derived, SylowC7 ⋊ C2×C5×C9×C47
HallC2×C5×C7×C47 ⋊ C9
HallC5×C7×C47 ⋊ C2×C9
HallC2×C7×C47 ⋊ C5×C9
HallC7×C47 ⋊ C2×C5×C9
HallC2×C5×C7 ⋊ C9×C47
HallC5×C7 ⋊ C2×C9×C47
HallC2×C7 ⋊ C5×C9×C47

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C47ΓL(1,𝔽8)
commutator, hypocenterC7C2×C5×C9×C47
FrattiniC3C2×C5×ΓL(1,𝔽8)×C47
Fitting, socle, prime radicalC2×C3×C5×C7×C47C3
cosocleC3×C7C2×C3×C5×C47
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C47

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29610

Conjugacy classes & character table

7050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 2);