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C43×D255 #36346703

order21930
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×D255
unambiguous semidirect productC3⋊(C43×D85)
unambiguous semidirect productC5⋊(C43×D51)
unambiguous semidirect productC17⋊(D15×C43)

Splittings

Fitting, socle, HallC3×C5×C17×C43 ⋊ C2
derived, HallC3×C5×C17 ⋊ C2×C43
HallC5×C17×C43 ⋊ D3
HallC3×C17×C43 ⋊ D5
HallC17×C43 ⋊ D15
HallC3×C5×C43 ⋊ D17
HallC5×C43 ⋊ D51
HallC3×C43 ⋊ D85
HallC5×C17 ⋊ D3×C43
HallC3×C17 ⋊ D5×C43
SylowC17 ⋊ D15×C43
HallC3×C5 ⋊ D17×C43
SylowC5 ⋊ C43×D51
SylowC3 ⋊ C43×D85

Subgroups

subgroupG/H
center, hypercenterC43D255
commutator, cosocle, hypocenterC3×C5×C17C2×C43
FrattiniC1G
Fitting, socleC3×C5×C17×C43C2
LCSG ▷ C3×C5×C17
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10965

Conjugacy classes & character table

5547 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21930, 16);