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C11×D35⋊D17 #39910469

order26180
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D35⋊D17
unambiguous semidirect productD35⋊(C11×D17)
unambiguous semidirect productD85⋊(C11×D7)
unambiguous semidirect productD119⋊(D5×C11)

Splittings

Fitting, socle, HallC5×C7×C11×C17 ⋊ C22
derived, HallC5×C7×C17 ⋊ C22×C11
HallC7×C11×C17 ⋊ C2×D5
HallC5×C11×C17 ⋊ C2×D7
HallC5×C7×C11 ⋊ C2×D17
HallC11×C17 ⋊ D5×D7
HallC7×C17 ⋊ C2×D5×C11
HallC5×C17 ⋊ C2×C11×D7
HallC7×C11 ⋊ D5×D17
HallC5×C11 ⋊ D7×D17
HallC5×C7 ⋊ C2×C11×D17
SylowC17 ⋊ D5×C11×D7
SylowC7 ⋊ D5×C11×D17
SylowC5 ⋊ C11×D7×D17

Subgroups

subgroupG/H
center, hypercenterC11D35⋊D17
commutator, cosocle, hypocenterC5×C7×C17C22×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C17C22
LCSG ▷ C5×C7×C17
UCSC1 ◁ C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6545

Conjugacy classes & character table

1892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 91);