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Cayley diagram

C8×C11⋊C5 #89149

order440
isoclinismisoclinic class of C11⋊C5
automorphismAut(G) = C22×AGL(1,𝔽11) (order 440) · Inn(G) = C11⋊C5 · Out(G) = C23
homologyAbelianization (H1) = C5×C8 · Schur multiplier (H2) = C1

Aliases

direct productC8×C11⋊C5
unambiguous semidirect product(C8×C11)⋊C5

Splittings

Fitting, HallC8×C11 ⋊ C5
derived, SylowC11 ⋊ C5×C8

Subgroups

subgroupG/H
center, hypercenterC8C11⋊C5
commutator, hypocenterC11C5×C8
FrattiniC4C2×C11⋊C5
FittingC8×C11C5
socleC2×C11C4×C5
prime radicalC2×C11⋊C5C4
cosocleC4×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C8

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 88

A minimal faithful permutation representation — 2 generators on 19 points:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C11⋊C5)⋊C16, C16×C11⋊C5, C8×AGL(1,𝔽11), …
maximal normal subgroup of(C11⋊C5)⋊C16, C16×C11⋊C5, C8×AGL(1,𝔽11), …
maximal quotient ofC16×C11⋊C5, C2×C8×C11⋊C5, C3⋊C8×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 2);