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C5×C9×D271 #37567246

order24390
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×D271

Splittings

Fitting, HallC5×C9×C271 ⋊ C2
derived, SylowC271 ⋊ C2×C5×C9
HallC9×C271 ⋊ C2×C5
HallC5×C271 ⋊ C2×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9D271
commutator, hypocenterC271C2×C5×C9
FrattiniC3C3×C5×D271
FittingC5×C9×C271C2
socleC3×C5×C271C2×C3
prime radicalC3×C5×D271C3
cosocleC3×C271C2×C3×C5
LCSG ▷ C271
UCSC1 ◁ C5×C9

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12195

Conjugacy classes & character table

6165 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24390, 5);