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C5×#76302 #14327672

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C24×C4

Aliases

direct productC5×#76302

Splittings

HallC3×C5 ⋊ #2354
SylowC3 ⋊ C5×#2354

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#390C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
cosocleC23×C3C24×C5
hypercenterC5×#390D3
hypocenterC3C5×#2354
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#390

1264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 53370);