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C9×D5×C373 #46777054

order33570
automorphism?
homologyAbelianization (H1) = C2×C9×C373 · Schur multiplier (H2) = C1

Aliases

direct productC9×D5×C373
unambiguous semidirect productC5⋊(C2×C9×C373)

Splittings

Fitting, HallC5×C9×C373 ⋊ C2
derived, SylowC5 ⋊ C2×C9×C373
HallC5×C373 ⋊ C2×C9
HallC5×C9 ⋊ C2×C373

Subgroups

subgroupG/H
center, hypercenterC9×C373D5
commutator, hypocenterC5C2×C9×C373
FrattiniC3C3×D5×C373
FittingC5×C9×C373C2
socleC3×C5×C373C2×C3
prime radicalC3×D5×C373C3
cosocleC3×C5C2×C3×C373
LCSG ▷ C5
UCSC1 ◁ C9×C373

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16785

Conjugacy classes & character table

13428 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33570, 4);