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Dic143 #10588103

order572
isoclinismisoclinic class of D143
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic143
unambiguous semidirect productC11⋊Dic13

Splittings

derived, HallC11×C13 ⋊ C4
SylowC13 ⋊ Dic11
SylowC11 ⋊ Dic13

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D143
commutator, hypocenterC11×C13C4
Fitting, socle, prime radical, cosocleC2×C11×C13C2
LCSG ▷ C11×C13
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 572

A minimal faithful permutation representation — 2 generators on 28 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)

Polycyclic presentation:

2^2,11,13|a^2=b,c^a=c^10,d^a=d^12

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×Dic11, D11×Dic13, #11765931, …
maximal normal subgroup ofD13×Dic11, D11×Dic13, #11765931, …
maximal quotient ofC11⋊#1055, C2×Dic143, C3×Dic143, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(572, 3);