Finite Group Databasebeta

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C5×C11×Dic153 #46777843

order33660
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic153
unambiguous semidirect productC9⋊(C5×C11×Dic17)

Splittings

derived, HallC9×C17 ⋊ C4×C5×C11
HallC5×C9×C11×C17 ⋊ C4
HallC9×C11×C17 ⋊ C4×C5
HallC5×C11×C17 ⋊ Dic9
HallC5×C9×C17 ⋊ C4×C11
HallC5×C9×C11 ⋊ Dic17
HallC11×C17 ⋊ C5×Dic9
HallC9×C11 ⋊ C5×Dic17
HallC5×C17 ⋊ C11×Dic9
HallC5×C9 ⋊ C11×Dic17
SylowC17 ⋊ C5×C11×Dic9
SylowC9 ⋊ C5×C11×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D153
commutator, hypocenterC9×C17C4×C5×C11
FrattiniC2×C3C5×C11×D51
FittingC2×C5×C9×C11×C17C2
socle, prime radicalC2×C3×C5×C11×C17D3
cosocleC2×C9×C17C2×C5×C11
LCSG ▷ C9×C17
UCSC1 ◁ C2×C5×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33660

Conjugacy classes & character table

8580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 11);