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C2×D221 #11725137

order884
isoclinismisoclinic class of D221
automorphismAut(G) order 84864
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD442
direct productC2×D221
unambiguous semidirect product(C2×C13)⋊D17
unambiguous semidirect product(C2×C17)⋊D13

Splittings

Fitting, socleC2×C13×C17 ⋊ C2
derived, HallC13×C17 ⋊ C22
SylowC17 ⋊ C2×D13
SylowC13 ⋊ C2×D17

Subgroups

subgroupG/H
center, hypercenterC2D221
commutator, cosocle, hypocenterC13×C17C22
FrattiniC1G
Fitting, socleC2×C13×C17C2
LCSG ▷ C13×C17
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 442

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13183729, #13183731, #13183732, …
maximal normal subgroup of#13183729, #13183731, #13183732, …
maximal quotient ofDic442, C4×D221, D884, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(884, 14);