Finite Group Databasebeta

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C9×C5⋊D5×C53 #37558702

order23850
automorphism?
homologyAbelianization (H1) = C2×C9×C53 · Schur multiplier (H2) = C5

Aliases

direct productC9×C5⋊D5×C53
unambiguous semidirect productC5⋊(C9×D5×C53)

Splittings

Fitting, HallC52×C9×C53 ⋊ C2
derived, SylowC52 ⋊ C2×C9×C53
HallC52×C53 ⋊ C2×C9
HallC52×C9 ⋊ C2×C53

Subgroups

subgroupG/H
center, hypercenterC9×C53C5⋊D5
commutator, hypocenterC52C2×C9×C53
FrattiniC3C3×C5⋊D5×C53
FittingC52×C9×C53C2
socleC3×C52×C53C2×C3
prime radicalC3×C5⋊D5×C53C3
cosocleC3×C52C2×C3×C53
LCSG ▷ C52
UCSC1 ◁ C9×C53

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11925

Conjugacy classes & character table

6678 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23850, 31);