Finite Group Databasebeta

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C5×Dic3×C19×C29 #45683246

order33060
automorphism?
homologyAbelianization (H1) = C4×C5×C19×C29 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×C19×C29
unambiguous semidirect productC3⋊(C4×C5×C19×C29)

Splittings

derived, SylowC3 ⋊ C4×C5×C19×C29
HallC3×C5×C19×C29 ⋊ C4
HallC3×C19×C29 ⋊ C4×C5
HallC3×C5×C29 ⋊ C4×C19
HallC3×C5×C19 ⋊ C4×C29
HallC3×C29 ⋊ C4×C5×C19
HallC3×C19 ⋊ C4×C5×C29
HallC3×C5 ⋊ C4×C19×C29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C19×C29D3
commutator, hypocenterC3C4×C5×C19×C29
FrattiniC2C5×D3×C19×C29
Fitting, socle, prime radicalC2×C3×C5×C19×C29C2
cosocleC2×C3C2×C5×C19×C29
LCSG ▷ C3
UCSC1 ◁ C2×C5×C19×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33060

Conjugacy classes & character table

16530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33060, 10);