Finite Group Databasebeta

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C72×C9×D17 #28418364

order14994
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C2×C72×C9 · Schur multiplier (H2) = C7

Aliases

direct productC72×C9×D17
unambiguous semidirect productC17⋊(C2×C72×C9)

Splittings

Fitting, HallC72×C9×C17 ⋊ C2
derived, SylowC17 ⋊ C2×C72×C9
HallC72×C17 ⋊ C2×C9
HallC9×C17 ⋊ C2×C72

Subgroups

subgroupG/H
center, hypercenterC72×C9D17
commutator, hypocenterC17C2×C72×C9
FrattiniC3C3×C72×D17
FittingC72×C9×C17C2
socleC3×C72×C17C2×C3
prime radicalC3×C72×D17C3
cosocleC3×C17C2×C3×C72
LCSG ▷ C17
UCSC1 ◁ C72×C9

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7497

Conjugacy classes & character table

4410 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC72×C9×#595, C7×C9×C7⋊#595, C7×C9×D7×D17, …
maximal normal subgroup ofC72×C9×#595, C7×C9×C7⋊#595, C7×C9×D7×D17, …
maximal quotient ofC72×C9×Dic17, C2×C72×C9×D17

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14994, 56);