Finite Group Databasebeta

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Cayley diagram

Dic119 #90911

order476
isoclinismisoclinic class of D119
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

dicyclicDic119
unambiguous semidirect productC7⋊Dic17

Splittings

derived, HallC7×C17 ⋊ C4
SylowC17 ⋊ Dic7
SylowC7 ⋊ Dic17

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D119
commutator, hypocenterC7×C17C4
Fitting, socle, prime radical, cosocleC2×C7×C17C2
LCSG ▷ C7×C17
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 476

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)(6,11)(7,10)(8,9)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)

Polycyclic presentation:

2^2,7,17|a^2=b,c^a=c^6,d^a=d^16

Conjugacy classes & character table

122 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic7×D17, D7×Dic17, #11745752, …
maximal normal subgroup ofDic7×D17, D7×Dic17, #11745752, …
maximal quotient ofC7⋊#3622, C2×Dic119, C3×Dic119, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(476, 3);