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C5×#79926 #14471603

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

Aliases

direct productC5×#79926

Splittings

FittingC3×C5×C8×Q8 ⋊ C2
HallC3×C5 ⋊ #3360
SylowC3 ⋊ C5×#3360

Subgroups

subgroupG/H
centerC22×C5C22×D12
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×C8×Q8C2
socleC22×C3×C5C22×D4
prime radicalC2×C5×D24C22
hypercenterC5×C8×Q8D3
hypocenterC3C5×#3360
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C4×C5×Q8 ◁ C5×C8×Q8

700 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 197301);