Finite Group Databasebeta

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C2×C7⋊C9×D121 #44478792

order30492
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7⋊C9×D121
unambiguous semidirect productC121⋊(C22×C7⋊C9)
unambiguous semidirect product(C2×C121)⋊(C2×C7⋊C9)
unambiguous semidirect product(C2×C7×D121)⋊C9

Splittings

derived, HallC7×C121 ⋊ C22×C9
HallC7⋊C9×C121 ⋊ C22
HallC2×C7×D121 ⋊ C9
SylowC121 ⋊ C22×C7⋊C9
SylowC7 ⋊ C2×C9×D121

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×D121
commutator, hypocenterC7×C121C22×C9
FrattiniC3×C11C2×ΓL(1,𝔽8)×D11
FittingC2×C3×C7×C121C2×C3
socleC2×C3×C7×C11C3×D11
prime radicalC2×C3×C7×D121C3
cosocleC3×C7×C121C22×C3
LCSG ▷ C7×C121
UCSC1 ◁ C2×C3

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15246

Conjugacy classes & character table

1860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 15);