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Cayley diagram

Dic102 #87988

order408
isoclinismisoclinic class of Dic102
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

dicyclicDic102

Splittings

HallC3×C17 ⋊ Q8
SylowC17 ⋊ Dic6
SylowC3 ⋊ Dic34

Subgroups

subgroupG/H
center, FrattiniC2C2×D51
commutator, socle, prime radical, cosocleC2×C3×C17C22
FittingC3×C4×C17C2
hypercenterC4D51
hypocenterC3×C17Q8
LCSG ▷ C2×C3×C17 ▷ C3×C17
UCSC1 ◁ C2 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 408

A minimal faithful permutation representation — 2 generators on 28 points:

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

Polycyclic presentation:

2^3,3,17|a^2=c,b^2=c,b^a=bc,d^a=d^2,e^a=e^16

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11717748, #11717750, #11717753, …
maximal normal subgroup of#11717748, #11717750, #11717753, …
maximal quotient of#11717803, C4⋊Dic51, C2×Dic102, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(408, 25);