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C5×D3×D391 #37553316

order23460
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×D391
unambiguous semidirect product(D3×C17)⋊(C5×D23)
unambiguous semidirect product(D3×C23)⋊(C5×D17)

Splittings

Fitting, socle, HallC3×C5×C17×C23 ⋊ C22
derived, HallC3×C17×C23 ⋊ C22×C5
HallC5×C17×C23 ⋊ C2×D3
HallC17×C23 ⋊ C2×C5×D3
HallC3×C5×C23 ⋊ C2×D17
HallC3×C5×C17 ⋊ C2×D23
HallC5×C23 ⋊ D3×D17
HallC5×C17 ⋊ D3×D23
HallC3×C23 ⋊ C2×C5×D17
HallC3×C17 ⋊ C2×C5×D23
SylowC23 ⋊ C5×D3×D17
SylowC17 ⋊ C5×D3×D23
HallC3×C5 ⋊ C2×D391
SylowC3 ⋊ C2×C5×D391

Subgroups

subgroupG/H
center, hypercenterC5D3×D391
commutator, cosocle, hypocenterC3×C17×C23C22×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C23C22
LCSG ▷ C3×C17×C23
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 5865

A minimal faithful permutation representation — 2 generators on 48 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42,43)(44,45,46,47,48);(1,2,4,6,8,10,12,14,16,18,20,22,23,21,19,17,15,13,11,9,7,5,3)(24,25,27,29,31,33,35,37,39,40,38,36,34,32,30,28,26)(42,43)

Conjugacy classes & character table

2955 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23460, 43);