Finite Group Databasebeta

← Prev (#90816) Next (#90818) →

Cayley diagram

C23×D29 #90817

order464
isoclinismisoclinic class of D29
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC23×D29
unambiguous semidirect productC29⋊C24
unambiguous semidirect product(C2×C29)⋊C23

Splittings

Fitting, socleC23×C29 ⋊ C2
derived, SylowC29 ⋊ C24

Subgroups

subgroupG/H
center, hypercenterC23D29
commutator, cosocle, hypocenterC29C24
FrattiniC1G
Fitting, socleC23×C29C2
LCSG ▷ C29
UCSC1 ◁ C23

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 232

A minimal faithful permutation representation — 4 generators on 35 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22⋊C4×D29, #11745244, C2×#90781, …
maximal normal subgroup ofC22⋊C4×D29, #11745244, C2×#90781, …
maximal quotient ofC22×Dic58, C22×C4×D29, C22×D116, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 50);