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Cayley diagram

C5×C11⋊C8 #89151

order440
isoclinismisoclinic class of D11
automorphismAut(G) = C22×C4×AGL(1,𝔽11) (order 1760) · Inn(G) = D11 · Out(G) = C22×C4×C5
homologyAbelianization (H1) = C5×C8 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11⋊C8

Splittings

derived, SylowC11 ⋊ C5×C8
HallC5×C11 ⋊ C8

Subgroups

subgroupG/H
center, hypercenterC4×C5D11
commutator, hypocenterC11C5×C8
FrattiniC4C5×D11
FittingC4×C5×C11C2
socle, prime radicalC2×C5×C11C4
cosocleC4×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C4×C5

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 440

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×C11⋊C8, #11724867, #11724869, …
maximal normal subgroup ofD5×C11⋊C8, #11724867, #11724869, …
maximal quotient ofC5×C11⋊C16, C2×C5×C11⋊C8, C3×C5×C11⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 4);