Finite Group Databasebeta

← Prev (#14638302) Next (#14638304) →

C11×#61110 #14638303

order2816
nilpotency class3
isoclinismisoclinic class of #61109
automorphism?
homologyAbelianization (H1) = C25×C11 · Schur multiplier (H2) = C29

Aliases

direct productC11×#61110

Subgroups

subgroupG/H
center, socleC2×C11C2×D42
commutator, Frattini, cosocleC2×C4C25×C11
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G

2684 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 176

A minimal faithful permutation representation — 5 generators on 27 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD11×#61110, #72269607
maximal subgroup ofD11×#61110, C11×#489347, #72269607
maximal normal subgroup ofD11×#61110, C11×#489347, #72269607

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 54098);