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C2×C3×C7×C11×D17 #30628183

order15708
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×C11×D17
unambiguous semidirect productC17⋊(C22×C3×C7×C11)
unambiguous semidirect product(C2×C17)⋊(C2×C3×C7×C11)

Splittings

Fitting, socleC2×C3×C7×C11×C17 ⋊ C2
derived, SylowC17 ⋊ C22×C3×C7×C11
HallC3×C7×C11×C17 ⋊ C22
HallC7×C11×C17 ⋊ C22×C3
HallC3×C11×C17 ⋊ C22×C7
HallC3×C7×C17 ⋊ C22×C11
HallC11×C17 ⋊ C22×C3×C7
HallC7×C17 ⋊ C22×C3×C11
HallC3×C17 ⋊ C22×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C11D17
commutator, cosocle, hypocenterC17C22×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C17C2
LCSG ▷ C17
UCSC1 ◁ C2×C3×C7×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7854

Conjugacy classes & character table

4620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 104);