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C5×#70101 #14298680

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

Aliases

direct productC5×#70101

Splittings

HallC3×C5 ⋊ #1830
SylowC3 ⋊ C5×#1830

Subgroups

subgroupG/H
centerC2×C5#4943
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C5×#101C2
socleC2×C3×C5#381
prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4C23×C5
hypercenterC2×C5×#101D3
hypocenterC3C5×#1830
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C2×C5×#101

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4,5)(7,8)(9,12)(10,16,17,23)(11,20)(13,25)(14,24)(15,28,19,34)(18,31,32,37)(21,36)(22,35)(26,38)(27,30)(29,39,33,40);(6,7,8)(9,11,14,22)(10,15,17,19)(12,20,24,35)(13,26,27,21)(16,28,23,34)(18,33,32,29)(25,38,30,36)(31,40,37,39);(9,10,13,18,14,17,27,32)(11,19,21,33,22,15,26,29)(12,23,25,37,24,16,30,31)(20,28,36,39,35,34,38,40)

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24378);