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C17×D555 #34038274

order18870
automorphism?
homologyAbelianization (H1) = C2×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D555
unambiguous semidirect productC3⋊(C17×D185)
unambiguous semidirect productC5⋊(C17×D111)
unambiguous semidirect productC37⋊(C17×D15)

Splittings

Fitting, socle, HallC3×C5×C17×C37 ⋊ C2
derived, HallC3×C5×C37 ⋊ C2×C17
HallC5×C17×C37 ⋊ D3
HallC3×C17×C37 ⋊ D5
HallC17×C37 ⋊ D15
HallC3×C5×C17 ⋊ D37
HallC5×C37 ⋊ D3×C17
HallC3×C37 ⋊ D5×C17
HallC5×C17 ⋊ D111
HallC3×C17 ⋊ D185
SylowC37 ⋊ C17×D15
HallC3×C5 ⋊ C17×D37
SylowC5 ⋊ C17×D111
SylowC3 ⋊ C17×D185

Subgroups

subgroupG/H
center, hypercenterC17D555
commutator, cosocle, hypocenterC3×C5×C37C2×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C37C2
LCSG ▷ C3×C5×C37
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9435

Conjugacy classes & character table

4743 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC17×D15×D37, D17×D555, D629⋊D15, …
maximal normal subgroup ofC17×D15×D37, D17×D555, D629⋊D15, …
maximal quotient ofC17×Dic555, C2×C17×D555

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18870, 15);