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C7×C9×Dic85 #36339175

order21420
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×Dic85

Splittings

derived, HallC5×C17 ⋊ C4×C7×C9
HallC5×C7×C9×C17 ⋊ C4
HallC7×C9×C17 ⋊ Dic5
HallC5×C9×C17 ⋊ C4×C7
HallC5×C7×C17 ⋊ C4×C9
HallC5×C7×C9 ⋊ Dic17
HallC9×C17 ⋊ C7×Dic5
HallC7×C17 ⋊ C9×Dic5
HallC5×C9 ⋊ C7×Dic17
HallC5×C7 ⋊ C9×Dic17
SylowC17 ⋊ C7×C9×Dic5
SylowC5 ⋊ C7×C9×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9D85
commutator, hypocenterC5×C17C4×C7×C9
FrattiniC2×C3C3×C7×D85
FittingC2×C5×C7×C9×C17C2
socle, prime radicalC2×C3×C5×C7×C17C2×C3
cosocleC2×C3×C5×C17C2×C3×C7
LCSG ▷ C5×C17
UCSC1 ◁ C2×C7×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21420

Conjugacy classes & character table

5544 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 7);