Finite Group Databasebeta

← Prev (#91026) Next (#91028) →

Cayley diagram

C3×#3957 #91027

order480
isoclinismisoclinic class of #686
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#3957

Splittings

FittingC3×C5×M16 ⋊ C2
HallC3×C5 ⋊ #104
SylowC5 ⋊ C3×#104

Subgroups

subgroupG/H
centerC3×C4C22⋊D5
commutatorC4×C5C2×C3×C4
FrattiniC2×C4C2×C3×D5
FittingC3×C5×M16C2
socleC2×C3×C5C22⋊C4
prime radicalC3×#709C2
cosocleC2×C4×C5C22×C3
hypercenterC3×M16D5
hypocenterC5C3×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×M16

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 2 generators on 16 points:

(1,2,4,5,3)(6,13,10,8,11,12,9,7)(14,15,16);(2,3)(4,5)(6,7)(8,11)(9,12)(10,13)

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11748174, #11748175, #11748204, …
maximal normal subgroup of#11748174, #11748175, #11748204, …
maximal quotient ofC3×#64684, C3×#64685, C3×#64687, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 103);