Finite Group Databasebeta

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C5×C9×D5×C53 #37558700

order23850
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C53 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D5×C53
unambiguous semidirect productC5⋊(C2×C5×C9×C53)

Splittings

Fitting, HallC52×C9×C53 ⋊ C2
derivedC5 ⋊ C2×C5×C9×C53
HallC52×C53 ⋊ C2×C9
HallC52×C9 ⋊ C2×C53
SylowC52 ⋊ C2×C9×C53

Subgroups

subgroupG/H
center, hypercenterC5×C9×C53D5
commutator, hypocenterC5C2×C5×C9×C53
FrattiniC3C3×C5×D5×C53
FittingC52×C9×C53C2
socleC3×C52×C53C2×C3
prime radicalC3×C5×D5×C53C3
cosocleC3×C5C2×C3×C5×C53
LCSG ▷ C5
UCSC1 ◁ C5×C9×C53

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4770

Conjugacy classes & character table

9540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23850, 29);