Finite Group Databasebeta

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C3×C5×Dic539 #44568305

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic539

Splittings

derived, HallC11×C49 ⋊ C3×C4×C5
HallC3×C5×C11×C49 ⋊ C4
HallC5×C11×C49 ⋊ C3×C4
HallC3×C11×C49 ⋊ C4×C5
HallC3×C5×C49 ⋊ Dic11
HallC5×C49 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ Dic49
HallC3×C49 ⋊ C5×Dic11
HallC5×C11 ⋊ C3×Dic49
SylowC49 ⋊ C3×C5×Dic11
HallC3×C11 ⋊ C5×Dic49
SylowC11 ⋊ C3×C5×Dic49

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D539
commutator, hypocenterC11×C49C3×C4×C5
FrattiniC2×C7C3×C5×D77
FittingC2×C3×C5×C11×C49C2
socle, prime radicalC2×C3×C5×C7×C11D7
cosocleC2×C11×C49C2×C3×C5
LCSG ▷ C11×C49
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32340

Conjugacy classes & character table

8130 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 7);