Finite Group Databasebeta

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C5×C11⋊#10597480 #46778043

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

Aliases

direct productC5×C11⋊#10597480

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derived, HallC32×C11×C17 ⋊ C4×C5
HallC5×C11×C17 ⋊ #157
HallC32×C5×C17 ⋊ Dic11
HallC32×C5×C11 ⋊ Dic17
HallC11×C17 ⋊ C5×#157
HallC32×C17 ⋊ C5×Dic11
HallC32×C11 ⋊ C5×Dic17
HallC5×C17 ⋊ C11⋊#157
HallC5×C11 ⋊ #10597480
HallC32×C5 ⋊ Dic187
SylowC17 ⋊ C5×C11⋊#157
SylowC11 ⋊ C5×#10597480
SylowC32 ⋊ C5×Dic187

Subgroups

subgroupG/H
center, hypercenterC5C11⋊#10597480
commutator, hypocenterC32×C11×C17C4×C5
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC5×C11×C17×C3⋊D3C2
cosocleC11×C17×C3⋊D3C2×C5
LCSG ▷ C32×C11×C17
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5610

Conjugacy classes & character table

2820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 211);