Finite Group Databasebeta

← Prev (#87759) Next (#87761) →

Cayley diagram

C23×D25 #87760

order400
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC23×D25
unambiguous semidirect productC25⋊C24
unambiguous semidirect product(C2×C25)⋊C23

Splittings

FittingC23×C25 ⋊ C2
derived, SylowC25 ⋊ C24

Subgroups

subgroupG/H
center, hypercenterC23D25
commutator, cosocle, hypocenterC25C24
FrattiniC5C23×D5
FittingC23×C25C2
socleC23×C5D5
LCSG ▷ C25
UCSC1 ◁ C23

201 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 200

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22⋊C4×D25, #11716444, C2×#87720, …
maximal normal subgroup ofC22⋊C4×D25, #11716444, C2×#87720, …
maximal quotient ofC22×Dic50, C22×C4×D25, C22×D100, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 54);