Finite Group Databasebeta

← Prev (#14520380) Next (#14520382) →

C9×C11×Dic5 #14520381

order1980
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×Dic5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C9×C11D5
commutator, hypocenterC5C4×C9×C11
FrattiniC2×C3C3×D5×C11
FittingC2×C5×C9×C11C2
socle, prime radicalC2×C3×C5×C11C2×C3
cosocleC2×C3×C5C2×C3×C11
LCSG ▷ C5
UCSC1 ◁ C2×C9×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 1980

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20)(21,22)(23,24)(25,26,27,28,29);(21,23,22,24)(26,29)(27,28)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC7×C9×C11×Dic5, C9×C11×Dic35, C11×Dic5×C7⋊C9, …
maximal normal subgroup ofC7×C9×C11×Dic5, C9×Dic5×C121, C9×C112×Dic5, …
maximal quotient ofC7×C9×C11×Dic5, C9×C11×Dic35, C11×Dic5×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 6);