Finite Group Databasebeta

C9×D109 #14520052

order1962
isoclinismisoclinic class of D109
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×D109

Splittings

Fitting, HallC9×C109 ⋊ C2
derived, SylowC109 ⋊ C2×C9

Subgroups

subgroupG/H
center, hypercenterC9D109
commutator, hypocenterC109C2×C9
FrattiniC3C3×D109
FittingC9×C109C2
socle, cosocleC3×C109C2×C3
prime radicalC3×D109C3
LCSG ▷ C109
UCSC1 ◁ C9

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 118
transitive degreeμt(G) = 981

A minimal faithful permutation representation — 2 generators on 118 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118);(11,118)(12,117)(13,116)(14,115)(15,114)(16,113)(17,112)(18,111)(19,110)(20,109)(21,108)(22,107)(23,106)(24,105)(25,104)(26,103)(27,102)(28,101)(29,100)(30,99)(31,98)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,90)(40,89)(41,88)(42,87)(43,86)(44,85)(45,84)(46,83)(47,82)(48,81)(49,80)(50,79)(51,78)(52,77)(53,76)(54,75)(55,74)(56,73)(57,72)(58,71)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC9×#89137, C9⋊#89137, D9×D109, …
maximal normal subgroup ofC9×#89137, C9⋊#89137, D9×D109, …
maximal quotient ofC9×Dic109, C2×C9×D109, C7×C9×D109, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1962, 4);