Finite Group Databasebeta

← Prev (#91400) Next (#91402) →

Cayley diagram

C4×#1200 #91401

order480
isoclinismisoclinic class of D3×D5
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#1200

Splittings

derived, HallC3×C5 ⋊ C2×C42
SylowC5 ⋊ C42×D3
SylowC3 ⋊ C42×D5

Subgroups

subgroupG/H
center, hypercenterC2×C4D3×D5
commutator, hypocenterC3×C5C2×C42
FrattiniC22C2×D3×D5
FittingC2×C3×C4×C5C22
socle, cosocleC22×C3×C5C23
prime radicalC22×D15C22
LCSG ▷ C3×C5
UCSC1 ◁ C2×C4

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC8×#1200, #11747583, #11747584, …
maximal normal subgroup ofC8×#1200, #11747583, #11747584, …
maximal quotient of#11746844, C4×#6648, #11746981, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 477);