Finite Group Databasebeta

← Prev (#90796) Next (#90798) →

Cayley diagram

C4×#1181 #90797

order464
isoclinismisoclinic class of #1181
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C4

Aliases

direct productC4×#1181

Splittings

FittingC4×C29 ⋊ C4
derived, SylowC29 ⋊ C42

Subgroups

subgroupG/H
center, hypercenterC4#1181
commutator, hypocenterC29C42
FrattiniC2C2×#1181
FittingC4×C29C4
socleC2×C29C2×C4
prime radical, cosocleC2×D29C22
LCSG ▷ C29
UCSC1 ◁ C4

30 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:

(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);(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)

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×#1181, #11745208, #11745224, …
maximal normal subgroup ofC8×#1181, #11745208, #11745224, …
maximal quotient ofC8×#1181, #11745208, C4×#6599, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 30);