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C5×#70045 #14301369

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#70045

Splittings

FittingC3×C5×#410 ⋊ C2
HallC3×C5 ⋊ #1884
SylowC3 ⋊ C5×#1884

Subgroups

subgroupG/H
centerC4×C5#882
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#410C2
socleC2×C3×C5#386
prime radicalC5×#5832C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#410D3
hypocenterC3C5×#1884
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C5×#410

664 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)(9,12)(10,16)(11,20)(13,19)(14,15)(17,22)(18,21)(23,24);(7,8)(9,11,13,16,14,22,24,21)(10,15,17,23,18,12,20,19);(9,10)(11,19,22,23)(12,16,15,21)(13,17)(14,18)(20,24)

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, 27067);