Finite Group Databasebeta

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Cayley diagram

C4×C22⋊D11 #66981

order352
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D11

Splittings

FittingC22×C4×C11 ⋊ C2
SylowC11 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D11
commutatorC2×C11C22×C4
FrattiniC22C22×D11
FittingC22×C4×C11C2
socle, cosocleC22×C11C23
prime radicalC2×C22⋊D11C2
hypercenterC22×C4D11
hypocenterC11C4×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 176

A minimal faithful permutation representation — 3 generators on 19 points:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C22⋊D11)⋊C8, #10622341, #10622342, …
maximal normal subgroup of(C22⋊D11)⋊C8, #10622341, #10622342, …
maximal quotient ofC4×Dic11⋊C4, #10622546, C4×(C2×D11)⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 123);