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C5×C9×Dic11 #14520380

order1980
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×Dic11

Splittings

derived, SylowC11 ⋊ C4×C5×C9
HallC5×C9×C11 ⋊ C4
HallC9×C11 ⋊ C4×C5
HallC5×C11 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D11
commutator, hypocenterC11C4×C5×C9
FrattiniC2×C3C3×C5×D11
FittingC2×C5×C9×C11C2
socle, prime radicalC2×C3×C5×C11C2×C3
cosocleC2×C3×C11C2×C3×C5
LCSG ▷ C11
UCSC1 ◁ C2×C5×C9

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);(15,17,16,18)(20,29)(21,28)(22,27)(23,26)(24,25)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C7×C9×Dic11, C5×C9×Dic77, C5×Dic11×C7⋊C9, …
maximal normal subgroup ofC5×C7×C9×Dic11, C5×C9×C11×Dic11, C5×C9×C13×Dic11, …
maximal quotient ofC5×C7×C9×Dic11, C5×C9×Dic77, C5×Dic11×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1980, 5);