Finite Group Databasebeta

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C5×#68751 #14312428

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#68751

Splittings

HallC3×C5 ⋊ #2102
SylowC3 ⋊ C5×#2102

Subgroups

subgroupG/H
centerC4×C5#885
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#339C2
socleC2×C3×C5#400
prime radicalC23×C3×C5#41
hypercenterC5×#339D3
hypocenterC3C5×#2102
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C5×#339

316 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)(9,12,13,16,14,22,18,10)(11,17,19,24,20,21,23,15);(9,11,18,19,14,20,13,23)(10,15,22,17,16,24,12,21);(7,8)(9,10,13,12,14,16,18,22)(11,17,19,24,20,21,23,15)

Conjugacy classes & character table

270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 38126);