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C5×#79894 #14458176

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

Aliases

direct productC5×#79894

Splittings

FittingC3×C5×#443 ⋊ C2
HallC3×C5 ⋊ #3292
SylowC3 ⋊ C5×#3292

Subgroups

subgroupG/H
centerC2×C5D4×D12
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#443C2
socleC2×C3×C5D42
hypercenterC5×#443D3
hypocenterC3C5×#3292
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#443

952 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)(9,11)(10,16)(12,22)(13,19)(14,20)(15,23)(17,24)(18,21);(7,8)(9,10)(11,16)(12,15)(13,21)(14,17)(18,19)(20,24)(22,23);(9,10,14,17)(11,18,20,23)(12,21,13,15)(16,22,24,19);(7,8)(10,15)(12,13)(16,23)(17,21)(18,24)(19,22)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 183874);