Finite Group Databasebeta

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C2×D5×C11×C17 #16836697

order3740
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C11×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×C11×C17
unambiguous semidirect productC5⋊(C22×C11×C17)
unambiguous semidirect product(C2×C5)⋊(C2×C11×C17)

Splittings

Fitting, socleC2×C5×C11×C17 ⋊ C2
derived, SylowC5 ⋊ C22×C11×C17
HallC5×C11×C17 ⋊ C22
HallC5×C17 ⋊ C22×C11
HallC5×C11 ⋊ C22×C17

Subgroups

subgroupG/H
center, hypercenterC2×C11×C17D5
commutator, cosocle, hypocenterC5C22×C11×C17
FrattiniC1G
Fitting, socleC2×C5×C11×C17C2
LCSG ▷ C5
UCSC1 ◁ C2×C11×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1870

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×D5×C11×C17, C2×C11×C17×D15, C2×C3×D5×C11×C17, …
maximal normal subgroup ofC2×C3×D5×C11×C17, C2×D5×C17×C11⋊C5, C2×C5×D5×C11×C17, …
maximal quotient ofD3×D5×C11×C17, C2×C11×C17×D15, C2×C3×D5×C11×C17, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3740, 43);