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C11×#208 #10587183

order528
isoclinismisoclinic class of Dic6
automorphismAut(G) = C22×C5×D3×D4 (order 960) · Inn(G) = C2×D3 · Out(G) = C24×C5
homologyAbelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#208

Splittings

HallC3×C11 ⋊ M16
SylowC3 ⋊ C11×M16

Subgroups

subgroupG/H
centerC4×C11C2×D3
commutatorC2×C3C2×C4×C11
FrattiniC4C2×D3×C11
FittingC2×C3×C4×C11C2
socleC2×C3×C11C2×C4
prime radicalC22×C3×C11C4
cosocleC3×C4C22×C11
hypercenterC2×C4×C11D3
hypocenterC3C11×M16
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C11 ◁ C2×C4×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 264

A minimal faithful permutation representation — 2 generators on 22 points:

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

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11760495, #11760497, #11760498, …
maximal normal subgroup of#11760495, #11760497, #11760498, …
maximal quotient ofC11×#803, C11×C4⋊(C3⋊C8), C11×#830, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 53);