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Cayley diagram

C22⋊D55 #89185

order440
isoclinismisoclinic class of Dic110
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productC22⋊D55

Splittings

FittingC22×C5×C11 ⋊ C2
HallC5×C11 ⋊ D4
SylowC11 ⋊ C22⋊D5
SylowC5 ⋊ C22⋊D11

Subgroups

subgroupG/H
center, FrattiniC2C2×D55
commutator, socle, cosocleC2×C5×C11C22
FittingC22×C5×C11C2
hypercenterC22D55
hypocenterC5×C11D4
LCSG ▷ C2×C5×C11 ▷ C5×C11
UCSC1 ◁ C2 ◁ C22

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 220

A minimal faithful permutation representation — 2 generators on 20 points:

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

Polycyclic presentation:

2^3,5,11|b^a=bc,d^a=d^4,e^a=e^10

Conjugacy classes & character table

113 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11724996, #11724999, D11×C22⋊D5, …
maximal normal subgroup of#11724996, #11724999, D11×C22⋊D5, …
maximal quotient of#11724930, #11724932, #11724933, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 38);