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Cayley diagram

C2×C5×Dic11 #89174

order440
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×Dic11

Splittings

derived, SylowC11 ⋊ C2×C4×C5
HallC5×C11 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC22×C5D11
commutator, hypocenterC11C2×C4×C5
FrattiniC2C2×C5×D11
Fitting, socle, prime radicalC22×C5×C11C2
cosocleC2×C11C22×C5
LCSG ▷ C11
UCSC1 ◁ C22×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 22
transitive degreeμt(G) = 440

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×Dic11, #11724885, #11724886, …
maximal normal subgroup ofDic5×Dic11, #11724885, #11724886, …
maximal quotient ofC2×C5×C11⋊C8, C5×#4318, C4×C5×Dic11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 27);