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C2×C3×C17×D77 #30628178

order15708
isoclinismisoclinic class of D77
automorphism?
homologyAbelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C17×D77
unambiguous semidirect product(C2×C11)⋊(C3×D7×C17)

Splittings

Fitting, socleC2×C3×C7×C11×C17 ⋊ C2
derived, HallC7×C11 ⋊ C22×C3×C17
HallC3×C7×C11×C17 ⋊ C22
HallC7×C11×C17 ⋊ C22×C3
HallC3×C11×C17 ⋊ C2×D7
HallC3×C7×C17 ⋊ C2×D11
HallC3×C7×C11 ⋊ C22×C17
HallC11×C17 ⋊ C2×C3×D7
HallC7×C17 ⋊ C2×C3×D11
HallC3×C11 ⋊ C2×D7×C17
HallC3×C7 ⋊ C2×C17×D11
SylowC11 ⋊ C2×C3×D7×C17
SylowC7 ⋊ C2×C3×C17×D11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D77
commutator, cosocle, hypocenterC7×C11C22×C3×C17
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C17C2
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7854

Conjugacy classes & character table

4080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 99);