Finite Group Databasebeta

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C5×C11×C19×Dic9 #49178303

order37620
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C19×Dic9
unambiguous semidirect productC9⋊(C4×C5×C11×C19)

Splittings

derived, SylowC9 ⋊ C4×C5×C11×C19
HallC5×C9×C11×C19 ⋊ C4
HallC9×C11×C19 ⋊ C4×C5
HallC5×C9×C19 ⋊ C4×C11
HallC5×C9×C11 ⋊ C4×C19
HallC9×C19 ⋊ C4×C5×C11
HallC9×C11 ⋊ C4×C5×C19
HallC5×C9 ⋊ C4×C11×C19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11×C19D9
commutator, hypocenterC9C4×C5×C11×C19
FrattiniC2×C3C5×D3×C11×C19
FittingC2×C5×C9×C11×C19C2
socle, prime radicalC2×C3×C5×C11×C19D3
cosocleC2×C9C2×C5×C11×C19
LCSG ▷ C9
UCSC1 ◁ C2×C5×C11×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

12540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 12);