Finite Group Databasebeta

← Prev (#92127) Next (#92129) →

Cayley diagram

C2×C3×C24⋊C5 #92128

order480
isoclinismisoclinic class of C24⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C22

Aliases

direct productC2×C3×C24⋊C5
unambiguous semidirect product(C25×C3)⋊C5

Splittings

Fitting, socle, HallC25×C3 ⋊ C5
derivedC24 ⋊ C2×C3×C5
SylowC25 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3C24⋊C5
commutator, cosocle, hypocenterC24C2×C3×C5
FrattiniC1G
Fitting, socleC25×C3C5
LCSG ▷ C24
UCSC1 ◁ C2×C3

164 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 13
transitive degreeμt(G) = 30

A minimal faithful permutation representation — 2 generators on 13 points:

(1,2,3)(4,7,8,11,12,5,6,9,10,13);(6,7)(8,9)

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

derived subgroup of#14514349, #14514352, #14514354, …
maximal subgroup ofC3×#66245, C3⋊#66245, Dic3×C24⋊C5, …
maximal normal subgroup ofC3×#66245, C3⋊#66245, Dic3×C24⋊C5, …
maximal quotient ofC3×C4×C24⋊C5, C2×C3×2−1+4⋊C5, C3×#585⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1204);