Finite Group Databasebeta

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C5×#5236 #11750735

order960
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#5236

Splittings

HallC3×C5 ⋊ #421
SylowC3 ⋊ C5×#421

Subgroups

subgroupG/H
centerC4×C5C2×#67
commutatorC3×C4C22×C4×C5
FrattiniC2×C4C22×C5×D3
Fitting, prime radicalC2×C3×C5×#41C2
socleC2×C3×C5C2×C22⋊C4
cosocleC2×C3×C4C23×C5
hypercenterC2×C5×#41D3
hypocenterC3C5×#421
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C2×C5×#41

308 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#72146, C5×#70295, #14297286, …
maximal normal subgroup ofC5×#72146, C5×#70295, #14297286, …
maximal quotient ofC5×#71639, C5×#71597, C5×#71621, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4930);