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Cayley diagram

C5×Dic24 #91044

order480
isoclinismisoclinic class of D48
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic24

Splittings

HallC3×C5 ⋊ Q32
SylowC3 ⋊ C5×Q32

Subgroups

subgroupG/H
centerC2×C5D24
commutator, cosocleC3×C8C22×C5
FrattiniC8C2×C5×D3
FittingC3×C5×C16C2
socle, prime radicalC2×C3×C5D8
hypercenterC5×C16D3
hypocenterC3C5×Q32
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×C16

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 2 generators on 40 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21)(22,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23)(38,39,40);(6,22,14,30)(7,23,15,31)(8,24,16,32)(9,25,17,33)(10,26,18,34)(11,27,19,35)(12,28,20,36)(13,29,21,37)(39,40)

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745821, #11745826, #11745827, …
maximal normal subgroup of#11745821, #11745826, #11745827, …
maximal quotient ofC5×#4503, C5×#4504, C2×C5×Dic24, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 120);