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C2×D207 #11718006

order828
isoclinismisoclinic class of D207
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD414
direct productC2×D207
unambiguous semidirect product(C2×C9)⋊D23
unambiguous semidirect product(C2×C23)⋊D9

Splittings

FittingC2×C9×C23 ⋊ C2
derived, HallC9×C23 ⋊ C22
SylowC23 ⋊ C2×D9
SylowC9 ⋊ C2×D23

Subgroups

subgroupG/H
center, hypercenterC2D207
commutator, cosocle, hypocenterC9×C23C22
FrattiniC3C2×D69
FittingC2×C9×C23C2
socleC2×C3×C23D3
LCSG ▷ C9×C23
UCSC1 ◁ C2

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 414

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2)(3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34);(4,11)(5,10)(6,9)(7,8)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD207⋊C4, #13110170, #13110173, …
maximal normal subgroup ofD207⋊C4, #13110170, #13110173, …
maximal quotient ofDic414, C4×D207, D828, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(828, 9);