Finite Group Databasebeta

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C5×C9×D5×C59 #40997806

order26550
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C59 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D5×C59
unambiguous semidirect productC5⋊(C2×C5×C9×C59)

Splittings

Fitting, HallC52×C9×C59 ⋊ C2
derivedC5 ⋊ C2×C5×C9×C59
HallC52×C59 ⋊ C2×C9
HallC52×C9 ⋊ C2×C59
SylowC52 ⋊ C2×C9×C59

Subgroups

subgroupG/H
center, hypercenterC5×C9×C59D5
commutator, hypocenterC5C2×C5×C9×C59
FrattiniC3C3×C5×D5×C59
FittingC52×C9×C59C2
socleC3×C52×C59C2×C3
prime radicalC3×C5×D5×C59C3
cosocleC3×C5C2×C3×C5×C59
LCSG ▷ C5
UCSC1 ◁ C5×C9×C59

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5310

Conjugacy classes & character table

10620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26550, 29);