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C5×#83782 #14411519

order1920
automorphism?
homologyAbelianization (H1) = C22×C42×C5 · Schur multiplier (H2) = C24×C4

Aliases

direct productC5×#83782

Splittings

HallC3×C5 ⋊ #2875
SylowC3 ⋊ C5×#2875

Subgroups

subgroupG/H
centerC2×C4×C5C23×D3
commutatorC2×C3C22×C42×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×#131C2
socleC22×C3×C5C23×C4
prime radicalC2×C3×C5×#41C22
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×#131D3
hypocenterC3C5×#2875
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C5×#131

1112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 28 points:

(1,2,3,4,5)(6,7,8)(15,21)(19,24)(22,27)(26,28);(13,15)(14,19)(16,22)(17,21)(18,24)(20,26)(23,27)(25,28);(7,8)(9,10,11,12)(14,18)(19,24)(20,25)(26,28);(13,14,16,20,17,18,23,25)(15,19,22,26,21,24,27,28)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 137217);