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C2×D209 #11719681

order836
isoclinismisoclinic class of D209
automorphismAut(G) order 75240
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD418
direct productC2×D209
unambiguous semidirect product(C2×C11)⋊D19
unambiguous semidirect product(C2×C19)⋊D11

Splittings

Fitting, socleC2×C11×C19 ⋊ C2
derived, HallC11×C19 ⋊ C22
SylowC19 ⋊ C2×D11
SylowC11 ⋊ C2×D19

Subgroups

subgroupG/H
center, hypercenterC2D209
commutator, cosocle, hypocenterC11×C19C22
FrattiniC1G
Fitting, socleC2×C11×C19C2
LCSG ▷ C11×C19
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 418

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

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD209⋊C4, #13131879, #13131880, …
maximal normal subgroup ofD209⋊C4, #13131879, #13131880, …
maximal quotient ofDic418, C4×D209, D836, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(836, 8);