Finite Group Databasebeta

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C3×C5×Dic551 #45683241

order33060
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic551

Splittings

derived, HallC19×C29 ⋊ C3×C4×C5
HallC3×C5×C19×C29 ⋊ C4
HallC5×C19×C29 ⋊ C3×C4
HallC3×C19×C29 ⋊ C4×C5
HallC3×C5×C29 ⋊ Dic19
HallC3×C5×C19 ⋊ Dic29
HallC5×C29 ⋊ C3×Dic19
HallC5×C19 ⋊ C3×Dic29
HallC3×C29 ⋊ C5×Dic19
HallC3×C19 ⋊ C5×Dic29
SylowC29 ⋊ C3×C5×Dic19
SylowC19 ⋊ C3×C5×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D551
commutator, hypocenterC19×C29C3×C4×C5
FrattiniC2C3×C5×D551
Fitting, socle, prime radicalC2×C3×C5×C19×C29C2
cosocleC2×C19×C29C2×C3×C5
LCSG ▷ C19×C29
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33060

Conjugacy classes & character table

8310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 5);