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C11×#15690392 #46778047

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

Aliases

direct productC11×#15690392

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derived, HallC32×C5×C17 ⋊ C4×C11
HallC32×C11×C17 ⋊ AGL(1,𝔽5)
HallC5×C11×C17 ⋊ #157
HallC32×C5×C11 ⋊ Dic17
HallC11×C17 ⋊ #4380
HallC32×C17 ⋊ C11×AGL(1,𝔽5)
HallC32×C11 ⋊ #66774
HallC5×C17 ⋊ C11×#157
HallC5×C11 ⋊ #10597480
HallC32×C5 ⋊ C11×Dic17
SylowC17 ⋊ C11×#4380
SylowC32 ⋊ C11×#66774
SylowC5 ⋊ C11×#10597480

Subgroups

subgroupG/H
center, hypercenterC11#15690392
commutator, hypocenterC32×C5×C17C4×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC11×C17×C3⋊D15C2
cosocleC17×C3⋊D15C2×C11
LCSG ▷ C32×C5×C17
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5610

Conjugacy classes & character table

2277 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 215);