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Dic235 #11745639

order940
isoclinismisoclinic class of D235
automorphismAut(G) order 86480
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic235
unambiguous semidirect productC47⋊Dic5

Splittings

derived, HallC5×C47 ⋊ C4
SylowC47 ⋊ Dic5
SylowC5 ⋊ Dic47

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D235
commutator, hypocenterC5×C47C4
Fitting, socle, prime radical, cosocleC2×C5×C47C2
LCSG ▷ C5×C47
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 940

A minimal faithful permutation representation — 2 generators on 56 points:

(1,2)(3,4)(5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56);(1,3,2,4)(6,9)(7,8)(11,56)(12,55)(13,54)(14,53)(15,52)(16,51)(17,50)(18,49)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)

Polycyclic presentation:

2^2,5,47|a^2=b,c^a=c^4,d^a=d^46

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×D47, D5×Dic47, #14273519, …
maximal normal subgroup ofDic5×D47, D5×Dic47, #14273519, …
maximal quotient ofC47⋊#168, C2×Dic235, C3×Dic235, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(940, 3);