Finite Group Databasebeta

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C5×C9×Dic97 #31775467

order17460
isoclinismisoclinic class of D97
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×Dic97

Splittings

derived, SylowC97 ⋊ C4×C5×C9
HallC5×C9×C97 ⋊ C4
HallC9×C97 ⋊ C4×C5
HallC5×C97 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D97
commutator, hypocenterC97C4×C5×C9
FrattiniC2×C3C3×C5×D97
FittingC2×C5×C9×C97C2
socle, prime radicalC2×C3×C5×C97C2×C3
cosocleC2×C3×C97C2×C3×C5
LCSG ▷ C97
UCSC1 ◁ C2×C5×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17460

Conjugacy classes & character table

4500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17460, 3);