Finite Group Databasebeta

← Prev (#14520376) Next (#14520378) →

Dic9×C11⋊C5 #14520377

order1980
isoclinismisoclinic class of D9×C11⋊C5
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productDic9×C11⋊C5
unambiguous semidirect productC9⋊(C4×C11⋊C5)
unambiguous semidirect product(C11×Dic9)⋊C5

Splittings

derived, HallC9×C11 ⋊ C4×C5
HallC9×C11⋊C5 ⋊ C4
HallC11×Dic9 ⋊ C5
SylowC11 ⋊ C5×Dic9
SylowC9 ⋊ C4×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2D9×C11⋊C5
commutator, hypocenterC9×C11C4×C5
FrattiniC2×C3D3×C11⋊C5
Fitting, cosocleC2×C9×C11C2×C5
socleC2×C3×C11C5×D3
prime radicalC2×C3×C11⋊C5D3
LCSG ▷ C9×C11
UCSC1 ◁ C2

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 396

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×Dic9×C11⋊C5, C11⋊C5×Dic63, Dic9×C121⋊C5, …
maximal normal subgroup ofC7×Dic9×C11⋊C5, C11×Dic9×C11⋊C5, C13×Dic9×C11⋊C5, …
maximal quotient ofC7×Dic9×C11⋊C5, C11⋊C5×Dic63, Dic9×C121⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 2);