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Cayley diagram

D5×Dic11 #89165

order440
isoclinismisoclinic class of D5×D11
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productD5×Dic11

Splittings

derived, HallC5×C11 ⋊ C2×C4
SylowC11 ⋊ C4×D5
SylowC5 ⋊ C2×Dic11

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D5×D11
commutator, hypocenterC5×C11C2×C4
Fitting, socle, cosocleC2×C5×C11C22
prime radicalC2×D5×C11C2
LCSG ▷ C5×C11
UCSC1 ◁ C2

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:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×Dic11, Dic11⋊AGL(1,𝔽5), D5×Dic22, …
maximal normal subgroup ofAGL(1,𝔽5)×Dic11, Dic11⋊AGL(1,𝔽5), D5×Dic22, …
maximal quotient ofD5×C11⋊C8, #11724869, Dic5×Dic11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 18);