Finite Group Databasebeta

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C17×Dic495 #46777848

order33660
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×Dic495
unambiguous semidirect productC9⋊(C17×Dic55)
unambiguous semidirect productC11⋊(C17×Dic45)

Splittings

derived, HallC5×C9×C11 ⋊ C4×C17
HallC5×C9×C11×C17 ⋊ C4
HallC9×C11×C17 ⋊ Dic5
HallC5×C11×C17 ⋊ Dic9
HallC5×C9×C17 ⋊ Dic11
HallC11×C17 ⋊ Dic45
HallC9×C17 ⋊ Dic55
HallC9×C11 ⋊ C17×Dic5
HallC5×C17 ⋊ Dic99
HallC5×C11 ⋊ C17×Dic9
HallC5×C9 ⋊ C17×Dic11
SylowC11 ⋊ C17×Dic45
SylowC9 ⋊ C17×Dic55
SylowC5 ⋊ C17×Dic99

Subgroups

subgroupG/H
center, hypercenterC2×C17D495
commutator, hypocenterC5×C9×C11C4×C17
FrattiniC2×C3C17×D165
FittingC2×C5×C9×C11×C17C2
socle, prime radicalC2×C3×C5×C11×C17D3
cosocleC2×C5×C9×C11C2×C17
LCSG ▷ C5×C9×C11
UCSC1 ◁ C2×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33660

Conjugacy classes & character table

8466 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 16);