Finite Group Databasebeta

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C7×C9×Dic121 #44478783

order30492
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×Dic121
unambiguous semidirect productC121⋊(C4×C7×C9)

Splittings

derived, SylowC121 ⋊ C4×C7×C9
HallC7×C9×C121 ⋊ C4
HallC9×C121 ⋊ C4×C7
HallC7×C121 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9D121
commutator, hypocenterC121C4×C7×C9
FrattiniC2×C3×C11C3×C7×D11
FittingC2×C7×C9×C121C2
socle, prime radicalC2×C3×C7×C11C3×D11
cosocleC2×C3×C121C2×C3×C7
LCSG ▷ C121
UCSC1 ◁ C2×C7×C9

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30492

Conjugacy classes & character table

7812 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 6);