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C11⋊C5×D97⋊C3 #44544984

order32010
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×D97⋊C3
unambiguous semidirect productD97⋊(C3×C11⋊C5)
unambiguous semidirect product(C97⋊C3)⋊(C2×C11⋊C5)
unambiguous semidirect product(C11×D97⋊C3)⋊C5
unambiguous semidirect product(C11⋊C5×D97)⋊C3

Splittings

Fitting, socle, derived, HallC11×C97 ⋊ C2×C3×C5
HallC11⋊C5×C97⋊C3 ⋊ C2
HallC11⋊C5×D97 ⋊ C3
HallC11×D97⋊C3 ⋊ C5
HallC11⋊C5×C97 ⋊ C2×C3
HallC11×C97⋊C3 ⋊ C2×C5
HallC11×D97 ⋊ C3×C5
HallC97⋊C3 ⋊ C2×C11⋊C5
HallD97 ⋊ C3×C11⋊C5
SylowC97 ⋊ C2×C3×C11⋊C5
SylowC11 ⋊ C5×D97⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C97C2×C3×C5
LCSG ▷ C11×C97
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1067

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 34);