Finite Group Databasebeta

← Prev (#92085) Next (#92087) →

Cayley diagram

C5×#1010 #92086

order480
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#1010

Splittings

FittingC3×C5×#41 ⋊ C2
HallC3×C5 ⋊ 2−1+4
SylowC3 ⋊ C5×2−1+4

Subgroups

subgroupG/H
centerC2×C5C23×D3
commutator, cosocleC2×C3C24×C5
FrattiniC2C23×C5×D3
FittingC3×C5×#41C2
socleC2×C3×C5C24
hypercenterC5×#41D3
hypocenterC3C5×2−1+4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C5×#41

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11749423, #11749458, #11749459, …
maximal normal subgroup of#11749423, #11749458, #11749459, …
maximal quotient ofC5×#5516, C5×#5518, C5×#5519, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1162);