Finite Group Databasebeta

← Prev (#92070) Next (#92072) →

Cayley diagram

C3×#4150 #92071

order480
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct productC3×#4150

Splittings

FittingC3×C5×#41 ⋊ C2
HallC3×C5 ⋊ 2−1+4
SylowC5 ⋊ C3×2−1+4

Subgroups

subgroupG/H
centerC2×C3C23×D5
commutator, cosocleC2×C5C24×C3
FrattiniC2C23×C3×D5
FittingC3×C5×#41C2
socleC2×C3×C5C24
hypercenterC3×#41D5
hypocenterC5C3×2−1+4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C3×#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:

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

Conjugacy classes & character table

111 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11749456, #11749457, #11749462, …
maximal normal subgroup of#11749456, #11749457, #11749462, …
maximal quotient ofC3×#65850, C3×#65852, C3×#65853, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1147);