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C5×#71820 #14313629

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#71820

Splittings

HallC3×C5 ⋊ #2132
SylowC3 ⋊ C5×#2132

Subgroups

subgroupG/H
centerC4×C5#834
commutatorC2×C3×C4C22×C4×C5
FrattiniC2×Q8C22×C5×D3
Fitting, prime radicalC3×C5×#532C2
socleC2×C3×C5C2×#99
cosocleC2×C3×Q8C23×C5
hypercenterC5×#532D3
hypocenterC3C5×#2132
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ C5×#532

500 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)(9,11,14,13)(10,16,19,18)(12,20,21,22)(15,23,17,24);(10,15)(12,21)(16,23)(17,19)(18,24)(20,22);(7,8)(9,10,13,18,14,19,11,16)(12,17,20,24,21,15,22,23)

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, 39327);