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Dic238 #11745766

order952
automorphismAut(G) order 91392
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

dicyclicDic238

Splittings

HallC7×C17 ⋊ Q8
SylowC17 ⋊ Dic14
SylowC7 ⋊ Dic34

Subgroups

subgroupG/H
center, FrattiniC2C2×D119
commutator, socle, prime radical, cosocleC2×C7×C17C22
FittingC4×C7×C17C2
hypercenterC4D119
hypocenterC7×C17Q8
LCSG ▷ C2×C7×C17 ▷ C7×C17
UCSC1 ◁ C2 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 952

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4)(5,8,7,6)(9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32);(1,5,3,7)(2,6,4,8)(10,15)(11,14)(12,13)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)

Polycyclic presentation:

2^3,7,17|a^2=c,b^2=c,b^a=bc,d^a=d^6,e^a=e^16

Conjugacy classes & character table

241 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14274035, #14274037, #14274040, …
maximal normal subgroup of#14274035, #14274037, #14274040, …
maximal quotient of#14274089, C4⋊Dic119, C2×Dic238, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(952, 24);