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C17×D645 #36346702

order21930
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D645
unambiguous semidirect productC3⋊(C17×D215)
unambiguous semidirect productC5⋊(C17×D129)
unambiguous semidirect productC43⋊(C17×D15)

Splittings

Fitting, socle, HallC3×C5×C17×C43 ⋊ C2
derived, HallC3×C5×C43 ⋊ C2×C17
HallC5×C17×C43 ⋊ D3
HallC3×C17×C43 ⋊ D5
HallC17×C43 ⋊ D15
HallC3×C5×C17 ⋊ D43
HallC5×C43 ⋊ D3×C17
HallC3×C43 ⋊ D5×C17
HallC5×C17 ⋊ D129
HallC3×C17 ⋊ D215
SylowC43 ⋊ C17×D15
HallC3×C5 ⋊ C17×D43
SylowC5 ⋊ C17×D129
SylowC3 ⋊ C17×D215

Subgroups

subgroupG/H
center, hypercenterC17D645
commutator, cosocle, hypocenterC3×C5×C43C2×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C43C2
LCSG ▷ C3×C5×C43
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10965

Conjugacy classes & character table

5508 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21930, 15);