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C5×#68232 #14281809

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

Aliases

direct productC5×#68232

Splittings

FittingC3×C5×Q8⋊C8 ⋊ C2
HallC3×C5 ⋊ #1481
SylowC3 ⋊ C5×#1481

Subgroups

subgroupG/H
centerC2×C4×C5D3×D4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×Q8⋊C8C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C5×D3C22⋊C4
cosocleC3×C42C23×C5
hypercenterC5×Q8⋊C8D3
hypocenterC3C5×#1481
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C42×C5 ◁ C5×Q8⋊C8

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 7507);