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C5×#80281 #14458104

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#80281

Splittings

FittingC3×C5×#453 ⋊ C2
HallC3×C5 ⋊ #3291
SylowC3 ⋊ C5×#3291

Subgroups

subgroupG/H
centerC2×C5#5590
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#453C2
socleC2×C3×C5D42
hypercenterC5×#453D3
hypocenterC3C5×#3291
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#453

920 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:

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

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 183802);