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D5×(C67⋊C3)⋊C11 #36348648

order22110
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productD5×(C67⋊C3)⋊C11
unambiguous semidirect productC5⋊(C2×(C67⋊C3)⋊C11)
unambiguous semidirect product(D5×C67⋊C3)⋊C11
unambiguous semidirect product(D5×C67⋊C11)⋊C3

Splittings

Fitting, socle, derived, HallC5×C67 ⋊ C2×C3×C11
HallC5×(C67⋊C3)⋊C11 ⋊ C2
HallD5×C67⋊C11 ⋊ C3
HallC5×C67⋊C11 ⋊ C2×C3
HallD5×C67⋊C3 ⋊ C11
HallC5×C67⋊C3 ⋊ C2×C11
HallC67⋊C11 ⋊ C3×D5
HallD5×C67 ⋊ C3×C11
HallC67⋊C3 ⋊ D5×C11
SylowC67 ⋊ C3×D5×C11
SylowC5 ⋊ C2×(C67⋊C3)⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C67C2×C3×C11
LCSG ▷ C5×C67
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 335

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22110, 44);