Finite Group Databasebeta

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C2×C7×D67⋊C9 #30683061

order16884
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D67⋊C9
unambiguous semidirect productD67⋊(C2×C7×C9)
unambiguous semidirect product(C2×D67)⋊(C7×C9)
unambiguous semidirect product(C67⋊C9)⋊(C22×C7)
unambiguous semidirect product(C2×C67⋊C9)⋊(C2×C7)

Splittings

derived, SylowC67 ⋊ C22×C7×C9
HallC7×C67⋊C9 ⋊ C22
HallC2×C7×D67 ⋊ C9
HallC67⋊C9 ⋊ C22×C7
HallC7×C67 ⋊ C22×C9
HallC2×D67 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D67⋊C3
commutator, hypocenterC67C22×C7×C9
FrattiniC3C2×C7×D67⋊C3
Fitting, socleC2×C3×C7×C67C2×C3
prime radicalC2×C3×C7×D67C3
cosocleC3×C67C22×C3×C7
LCSG ▷ C67
UCSC1 ◁ C2×C3×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8442

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16884, 30);