Finite Group Databasebeta

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C3×C5×Dic561 #46777978

order33660
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic561
unambiguous semidirect productC3⋊(C3×C5×Dic187)

Splittings

derivedC3×C11×C17 ⋊ C3×C4×C5
HallC32×C5×C11×C17 ⋊ C4
HallC32×C11×C17 ⋊ C4×C5
HallC5×C11×C17 ⋊ C3×Dic3
HallC32×C5×C17 ⋊ Dic11
HallC32×C5×C11 ⋊ Dic17
HallC11×C17 ⋊ C3×C5×Dic3
HallC32×C17 ⋊ C5×Dic11
HallC32×C11 ⋊ C5×Dic17
HallC5×C17 ⋊ C3×Dic33
HallC5×C11 ⋊ C3×Dic51
HallC32×C5 ⋊ Dic187
SylowC17 ⋊ C3×C5×Dic33
SylowC11 ⋊ C3×C5×Dic51
SylowC32 ⋊ C5×Dic187

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D561
commutator, hypocenterC3×C11×C17C3×C4×C5
FrattiniC2C3×C5×D561
Fitting, socle, prime radicalC2×C32×C5×C11×C17C2
cosocleC2×C3×C11×C17C2×C3×C5
LCSG ▷ C3×C11×C17
UCSC1 ◁ C2×C3×C5

112 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11220

Conjugacy classes & character table

8460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 146);