Finite Group Databasebeta

← Prev (#49178307) Next (#49178309) →

C11×Dic855 #49178308

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

Aliases

direct productC11×Dic855
unambiguous semidirect productC9⋊(C11×Dic95)
unambiguous semidirect productC19⋊(C11×Dic45)

Splittings

derived, HallC5×C9×C19 ⋊ C4×C11
HallC5×C9×C11×C19 ⋊ C4
HallC9×C11×C19 ⋊ Dic5
HallC5×C11×C19 ⋊ Dic9
HallC5×C9×C11 ⋊ Dic19
HallC11×C19 ⋊ Dic45
HallC9×C19 ⋊ C11×Dic5
HallC9×C11 ⋊ Dic95
HallC5×C19 ⋊ C11×Dic9
HallC5×C11 ⋊ Dic171
HallC5×C9 ⋊ C11×Dic19
SylowC19 ⋊ C11×Dic45
SylowC9 ⋊ C11×Dic95
SylowC5 ⋊ C11×Dic171

Subgroups

subgroupG/H
center, hypercenterC2×C11D855
commutator, hypocenterC5×C9×C19C4×C11
FrattiniC2×C3C11×D285
FittingC2×C5×C9×C11×C19C2
socle, prime radicalC2×C3×C5×C11×C19D3
cosocleC2×C5×C9×C19C2×C11
LCSG ▷ C5×C9×C19
UCSC1 ◁ C2×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

9438 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 17);