Finite Group Databasebeta

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Cayley diagram

Q16×D11 #66970

order352
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productQ16×D11

Splittings

FittingC11×Q16 ⋊ C2
SylowC11 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC2D4×D11
commutator, cosocleC4×C11C23
FrattiniC4C22×D11
FittingC11×Q16C2
socleC2×C11C2×D4
prime radicalC2×D11D4
hypercenterQ16D11
hypocenterC11C2×Q16
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C4 ◁ Q16

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 176

A minimal faithful permutation representation — 3 generators on 27 points:

(2,3)(4,5)(6,7)(8,9)(10,11);(1,2,4,6,8,10,11,9,7,5,3)(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20);(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21)

Conjugacy classes & character table

49 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD11×SD32, #10622528, D11×Q32, …
maximal normal subgroup ofD11×SD32, #10622528, D11×Q32, …
maximal quotient of#10622403, #10622405, #10622406, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 112);