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C17×D35⋊D11 #39910478

order26180
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productC17×D35⋊D11
unambiguous semidirect productD35⋊(C17×D11)
unambiguous semidirect productD55⋊(D7×C17)
unambiguous semidirect productD77⋊(D5×C17)

Splittings

Fitting, socle, HallC5×C7×C11×C17 ⋊ C22
derived, HallC5×C7×C11 ⋊ C22×C17
HallC7×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D11
HallC11×C17 ⋊ D5×D7
HallC7×C17 ⋊ D5×D11
HallC5×C17 ⋊ D7×D11
HallC7×C11 ⋊ C2×D5×C17
HallC5×C11 ⋊ C2×D7×C17
HallC5×C7 ⋊ C2×C17×D11
SylowC11 ⋊ D5×D7×C17
SylowC7 ⋊ D5×C17×D11
SylowC5 ⋊ D7×C17×D11

Subgroups

subgroupG/H
center, hypercenterC17D35⋊D11
commutator, cosocle, hypocenterC5×C7×C11C22×C17
FrattiniC1G
Fitting, socleC5×C7×C11×C17C22
LCSG ▷ C5×C7×C11
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6545

Conjugacy classes & character table

1955 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 100);