Finite Group Databasebeta

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C9×Dic5×C59 #24902860

order10620
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C4×C9×C59 · Schur multiplier (H2) = C1

Aliases

direct productC9×Dic5×C59

Splittings

derived, SylowC5 ⋊ C4×C9×C59
HallC5×C9×C59 ⋊ C4
HallC5×C59 ⋊ C4×C9
HallC5×C9 ⋊ C4×C59

Subgroups

subgroupG/H
center, hypercenterC2×C9×C59D5
commutator, hypocenterC5C4×C9×C59
FrattiniC2×C3C3×D5×C59
FittingC2×C5×C9×C59C2
socle, prime radicalC2×C3×C5×C59C2×C3
cosocleC2×C3×C5C2×C3×C59
LCSG ▷ C5
UCSC1 ◁ C2×C9×C59

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10620, 3);