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C3×C5×C23×D51 #47976103

order35190
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C23×D51
unambiguous semidirect productC3⋊(C3×C5×C23×D17)
unambiguous semidirect productC17⋊(C3×C5×D3×C23)

Splittings

Fitting, socle, HallC32×C5×C17×C23 ⋊ C2
derivedC3×C17 ⋊ C2×C3×C5×C23
HallC32×C17×C23 ⋊ C2×C5
HallC5×C17×C23 ⋊ C3×D3
HallC32×C5×C23 ⋊ D17
HallC32×C5×C17 ⋊ C2×C23
HallC17×C23 ⋊ C3×C5×D3
HallC32×C23 ⋊ C5×D17
HallC32×C17 ⋊ C2×C5×C23
HallC5×C17 ⋊ C3×D3×C23
HallC32×C5 ⋊ C23×D17
SylowC17 ⋊ C3×C5×D3×C23
SylowC32 ⋊ C5×C23×D17

Subgroups

subgroupG/H
center, hypercenterC3×C5×C23D51
commutator, cosocle, hypocenterC3×C17C2×C3×C5×C23
FrattiniC1G
Fitting, socleC32×C5×C17×C23C2
LCSG ▷ C3×C17
UCSC1 ◁ C3×C5×C23

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11730

Conjugacy classes & character table

9315 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35190, 27);