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C11×#33688 #14610881

order2816
nilpotency class4
isoclinismisoclinic class of #33688
automorphism?
homologyAbelianization (H1) = C24×C11 · Schur multiplier (H2) = C24

Aliases

direct productC11×#33688

Subgroups

subgroupG/H
center, socleC2×C11#3109
commutator, Frattini, cosocleC2×C8C24×C11
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C11×M16 ◁ G

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 27 points:

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

Conjugacy classes & character table

374 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofD11×#33688, #72269603
maximal subgroup ofD11×#33688, C11×#489347, #72269603
maximal normal subgroup ofD11×#33688, C11×#489347, #72269603

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 26676);