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Dic138 #10587785

order552
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

dicyclicDic138

Splittings

HallC3×C23 ⋊ Q8
SylowC23 ⋊ Dic6
SylowC3 ⋊ Dic46

Subgroups

subgroupG/H
center, FrattiniC2C2×D69
commutator, socle, prime radical, cosocleC2×C3×C23C22
FittingC3×C4×C23C2
hypercenterC4D69
hypocenterC3×C23Q8
LCSG ▷ C2×C3×C23 ▷ C3×C23
UCSC1 ◁ C2 ◁ C4

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 552

A minimal faithful permutation representation — 2 generators on 34 points:

(1,2,3,4)(5,8,7,6)(9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34);(1,5,3,7)(2,6,4,8)(10,11)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)

Polycyclic presentation:

2^3,3,23|a^2=c,b^2=c,b^a=bc,d^a=d^2,e^a=e^22

Conjugacy classes & character table

141 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11764141, #11764143, #11764146, …
maximal normal subgroup of#11764141, #11764143, #11764146, …
maximal quotient of#11764196, C4⋊Dic69, C2×Dic138, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(552, 23);