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C2×D235 #11745646

order940
isoclinismisoclinic class of D235
automorphismAut(G) order 86480
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD470
direct productC2×D235
unambiguous semidirect product(C2×C5)⋊D47
unambiguous semidirect product(C2×C47)⋊D5

Splittings

Fitting, socleC2×C5×C47 ⋊ C2
derived, HallC5×C47 ⋊ C22
SylowC47 ⋊ C2×D5
SylowC5 ⋊ C2×D47

Subgroups

subgroupG/H
center, hypercenterC2D235
commutator, cosocle, hypocenterC5×C47C22
FrattiniC1G
Fitting, socleC2×C5×C47C2
LCSG ▷ C5×C47
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 54
transitive degreeμt(G) = 470

A minimal faithful permutation representation — 2 generators on 54 points:

(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54);(4,7)(5,6)(9,54)(10,53)(11,52)(12,51)(13,50)(14,49)(15,48)(16,47)(17,46)(18,45)(19,44)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14273518, #14273520, #14273521, …
maximal normal subgroup of#14273518, #14273520, #14273521, …
maximal quotient ofDic470, C4×D235, D940, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(940, 10);