Finite Group Databasebeta

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C3×C5×Dic529 #44540664

order31740
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic529
unambiguous semidirect productC529⋊(C3×C4×C5)

Splittings

derived, SylowC529 ⋊ C3×C4×C5
HallC3×C5×C529 ⋊ C4
HallC5×C529 ⋊ C3×C4
HallC3×C529 ⋊ C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D529
commutator, hypocenterC529C3×C4×C5
FrattiniC2×C23C3×C5×D23
FittingC2×C3×C5×C529C2
socle, prime radicalC2×C3×C5×C23D23
cosocleC2×C529C2×C3×C5
LCSG ▷ C529
UCSC1 ◁ C2×C3×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31740

Conjugacy classes & character table

7980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31740, 2);