Finite Group Databasebeta

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C4×C7×C67⋊C9 #30683033

order16884
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7×C67⋊C9
unambiguous semidirect product(C4×C67)⋊(C7×C9)

Splittings

derived, SylowC67 ⋊ C4×C7×C9
HallC4×C7×C67 ⋊ C9
HallC7×C67 ⋊ C4×C9
HallC4×C67 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4×C7C67⋊C3
commutator, hypocenterC67C4×C7×C9
FrattiniC2×C3C2×C7×C67⋊C3
FittingC3×C4×C7×C67C3
socle, prime radicalC2×C3×C7×C67C2×C3
cosocleC2×C3×C67C2×C3×C7
LCSG ▷ C67
UCSC1 ◁ C3×C4×C7

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16884

Conjugacy classes & character table

2100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16884, 2);