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C5×Dic9×C131 #37556031

order23580
automorphism?
homologyAbelianization (H1) = C4×C5×C131 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic9×C131
unambiguous semidirect productC9⋊(C4×C5×C131)

Splittings

derived, SylowC9 ⋊ C4×C5×C131
HallC5×C9×C131 ⋊ C4
HallC9×C131 ⋊ C4×C5
HallC5×C9 ⋊ C4×C131

Subgroups

subgroupG/H
center, hypercenterC2×C5×C131D9
commutator, hypocenterC9C4×C5×C131
FrattiniC2×C3C5×D3×C131
FittingC2×C5×C9×C131C2
socle, prime radicalC2×C3×C5×C131D3
cosocleC2×C9C2×C5×C131
LCSG ▷ C9
UCSC1 ◁ C2×C5×C131

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23580

Conjugacy classes & character table

7860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23580, 6);