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Cayley diagram

C4⋊Dic29 #90780

order464
isoclinismisoclinic class of Dic58
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productC4⋊Dic29

Splittings

SylowC29 ⋊ C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C2×D29
commutatorC2×C29C2×C4
FittingC2×C4×C29C2
socle, prime radical, cosocleC22×C29C22
hypercenterC2×C4D29
hypocenterC29C4⋊C4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C4

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 37
transitive degreeμt(G) = 464

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(34,35,36,37);(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)(28,29)(30,31,32,33)(35,37)

Polycyclic presentation:

2^4,29|a^2=c,b^2=d,b^a=bd,e^a=e^28

Conjugacy classes & character table

122 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745155, #11745156, #11745164, …
maximal normal subgroup of#11745155, #11745156, #11745164, …
maximal quotient ofC4⋊#6597, #11745165, #11745166, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 13);