Finite Group Databasebeta

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C9×C11×C19×Dic5 #49178299

order37620
automorphism?
homologyAbelianization (H1) = C4×C9×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×C19×Dic5

Splittings

derived, SylowC5 ⋊ C4×C9×C11×C19
HallC5×C9×C11×C19 ⋊ C4
HallC5×C11×C19 ⋊ C4×C9
HallC5×C9×C19 ⋊ C4×C11
HallC5×C9×C11 ⋊ C4×C19
HallC5×C19 ⋊ C4×C9×C11
HallC5×C11 ⋊ C4×C9×C19
HallC5×C9 ⋊ C4×C11×C19

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11×C19D5
commutator, hypocenterC5C4×C9×C11×C19
FrattiniC2×C3C3×D5×C11×C19
FittingC2×C5×C9×C11×C19C2
socle, prime radicalC2×C3×C5×C11×C19C2×C3
cosocleC2×C3×C5C2×C3×C11×C19
LCSG ▷ C5
UCSC1 ◁ C2×C9×C11×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

15048 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 8);