Finite Group Databasebeta

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C11×#89205 #18012925

order4851
isoclinismisoclinic class of #3862
automorphism?
homologyAbelianization (H1) = C9×C11 · Schur multiplier (H2) = C7

Aliases

direct productC11×#89205

Splittings

derived, SylowC72 ⋊ C9×C11
HallC72×C11 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC3×C11#3862
commutator, hypocenterC72C9×C11
FrattiniC3C11×#3862
Fitting, socle, prime radicalC3×C72×C11C3
cosocleC3×C72C3×C11
LCSG ▷ C72
UCSC1 ◁ C3×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 693

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14,15)(16,18,17)(20,21,22)(23,25,24)(26,27,29,28,30,32,31,33,34);(12,13,15,17,14,16,18)(19,20,21,23,22,24,25)

Conjugacy classes & character table

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

Relationships

derived subgroup ofC11⋊#13183527, #11725071⋊D11, #34084675, …
maximal subgroup ofC11×C22⋊#89205, C11⋊C5×#89205, C5×C11×#89205
maximal normal subgroup ofC11⋊C5×#89205, C5×C11×#89205
maximal quotient ofC11×C22⋊#89205, C5×C11×#89205

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4851, 8);