Finite Group Databasebeta

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C19×Dic495 #49178309

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

Aliases

direct productC19×Dic495
unambiguous semidirect productC9⋊(C19×Dic55)
unambiguous semidirect productC11⋊(C19×Dic45)

Splittings

derived, HallC5×C9×C11 ⋊ C4×C19
HallC5×C9×C11×C19 ⋊ C4
HallC9×C11×C19 ⋊ Dic5
HallC5×C11×C19 ⋊ Dic9
HallC5×C9×C19 ⋊ Dic11
HallC11×C19 ⋊ Dic45
HallC9×C19 ⋊ Dic55
HallC9×C11 ⋊ C19×Dic5
HallC5×C19 ⋊ Dic99
HallC5×C11 ⋊ C19×Dic9
HallC5×C9 ⋊ C19×Dic11
SylowC11 ⋊ C19×Dic45
SylowC9 ⋊ C19×Dic55
SylowC5 ⋊ C19×Dic99

Subgroups

subgroupG/H
center, hypercenterC2×C19D495
commutator, hypocenterC5×C9×C11C4×C19
FrattiniC2×C3C19×D165
FittingC2×C5×C9×C11×C19C2
socle, prime radicalC2×C3×C5×C11×C19D3
cosocleC2×C5×C9×C11C2×C19
LCSG ▷ C5×C9×C11
UCSC1 ◁ C2×C19

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

9462 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 18);