Finite Group Databasebeta

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C5×C9×Dic85 #29505672

order15300
isoclinismisoclinic class of D85
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×Dic85

Splittings

derivedC5×C17 ⋊ C4×C5×C9
HallC52×C9×C17 ⋊ C4
HallC52×C17 ⋊ C4×C9
HallC52×C9 ⋊ Dic17
HallC9×C17 ⋊ C5×Dic5
SylowC52 ⋊ C9×Dic17
SylowC17 ⋊ C5×C9×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D85
commutator, hypocenterC5×C17C4×C5×C9
FrattiniC2×C3C3×C5×D85
FittingC2×C52×C9×C17C2
socle, prime radicalC2×C3×C52×C17C2×C3
cosocleC2×C3×C5×C17C2×C3×C5
LCSG ▷ C5×C17
UCSC1 ◁ C2×C5×C9

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3060

Conjugacy classes & character table

3960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 58);