Finite Group Databasebeta

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C5×Dic3×C529 #44540667

order31740
automorphism?
homologyAbelianization (H1) = C4×C5×C529 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×C529
unambiguous semidirect productC3⋊(C4×C5×C529)

Splittings

derived, SylowC3 ⋊ C4×C5×C529
HallC3×C5×C529 ⋊ C4
HallC3×C529 ⋊ C4×C5
HallC3×C5 ⋊ C4×C529

Subgroups

subgroupG/H
center, hypercenterC2×C5×C529D3
commutator, hypocenterC3C4×C5×C529
FrattiniC2×C23C5×D3×C23
FittingC2×C3×C5×C529C2
socle, prime radicalC2×C3×C5×C23C2×C23
cosocleC2×C3×C23C2×C5×C23
LCSG ▷ C3
UCSC1 ◁ C2×C5×C529

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31740

Conjugacy classes & character table

15870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31740, 5);