Finite Group Databasebeta

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C7×C9×Dic59 #28415474

order14868
isoclinismisoclinic class of D59
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×Dic59
unambiguous semidirect productC59⋊(C4×C7×C9)

Splittings

derived, SylowC59 ⋊ C4×C7×C9
HallC7×C9×C59 ⋊ C4
HallC9×C59 ⋊ C4×C7
HallC7×C59 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9D59
commutator, hypocenterC59C4×C7×C9
FrattiniC2×C3C3×C7×D59
FittingC2×C7×C9×C59C2
socle, prime radicalC2×C3×C7×C59C2×C3
cosocleC2×C3×C59C2×C3×C7
LCSG ▷ C59
UCSC1 ◁ C2×C7×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14868

Conjugacy classes & character table

3906 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14868, 3);