Finite Group Databasebeta

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Cayley diagram

C4⋊#1181 #90798

order464
isoclinismisoclinic class of #90796
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productC4⋊#1181

Splittings

FittingC4×C29 ⋊ C4
SylowC29 ⋊ C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC2C2×#1181
commutator, socleC2×C29C2×C4
FittingC4×C29C4
prime radical, cosocleC2×D29C22
hypercenterC4#1181
hypocenterC29C4⋊C4
LCSG ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C4

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 116

A minimal faithful permutation representation — 2 generators on 33 points:

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

Polycyclic presentation:

2^4,29|a^2=c,b^2=d,b^a=bd,e^a=e^12,e^c=e^28

Conjugacy classes & character table

38 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745209, #11745210, #11745223, …
maximal normal subgroup of#11745209, #11745210, #11745223, …
maximal quotient of#11745209, #11745210, #11745211, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 31);