Finite Group Databasebeta

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D5×D11×C37⋊C3 #37567555

order24420
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD5×D11×C37⋊C3
unambiguous semidirect product(D5×C11)⋊(C2×C37⋊C3)
unambiguous semidirect product(C5×D11)⋊(C2×C37⋊C3)
unambiguous semidirect productD55⋊(C2×C37⋊C3)
unambiguous semidirect product(D5×D11×C37)⋊C3

Splittings

Fitting, socle, derived, HallC5×C11×C37 ⋊ C22×C3
HallD5×D11×C37 ⋊ C3
HallC5×C11×C37⋊C3 ⋊ C22
HallC11×C37⋊C3 ⋊ C2×D5
HallC5×C37⋊C3 ⋊ C2×D11
HallC11×C37 ⋊ C2×C3×D5
HallC5×C37 ⋊ C2×C3×D11
HallC5×C11 ⋊ C22×C37⋊C3
SylowC37 ⋊ C3×D5×D11
SylowC11 ⋊ C2×D5×C37⋊C3
SylowC5 ⋊ C2×D11×C37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C11×C37C22×C3
LCSG ▷ C5×C11×C37
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2035

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 76);