Finite Group Databasebeta

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C5×C11×C17×#157 #46778038

order33660
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C17 · Schur multiplier (H2) = C3

Aliases

direct productC5×C11×C17×#157

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derived, SylowC32 ⋊ C4×C5×C11×C17
HallC32×C11×C17 ⋊ C4×C5
HallC32×C5×C17 ⋊ C4×C11
HallC32×C5×C11 ⋊ C4×C17
HallC32×C17 ⋊ C4×C5×C11
HallC32×C11 ⋊ C4×C5×C17
HallC32×C5 ⋊ C4×C11×C17

Subgroups

subgroupG/H
center, hypercenterC5×C11×C17#157
commutator, hypocenterC32C4×C5×C11×C17
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC5×C11×C17×C3⋊D3C2
cosocleC3⋊D3C2×C5×C11×C17
LCSG ▷ C32
UCSC1 ◁ C5×C11×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5610

Conjugacy classes & character table

5610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 206);