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C7×Dic9×C121 #44478786

order30492
automorphism?
homologyAbelianization (H1) = C4×C7×C121 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic9×C121
unambiguous semidirect productC9⋊(C4×C7×C121)

Splittings

derived, SylowC9 ⋊ C4×C7×C121
HallC7×C9×C121 ⋊ C4
HallC9×C121 ⋊ C4×C7
HallC7×C9 ⋊ C4×C121

Subgroups

subgroupG/H
center, hypercenterC2×C7×C121D9
commutator, hypocenterC9C4×C7×C121
FrattiniC2×C3×C11D3×C7×C11
FittingC2×C7×C9×C121C2
socle, prime radicalC2×C3×C7×C11D3×C11
cosocleC2×C9×C11C2×C7×C11
LCSG ▷ C9
UCSC1 ◁ C2×C7×C121

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30492

Conjugacy classes & character table

10164 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 9);