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D7×(C67⋊C3)⋊C11 #44526284

order30954
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productD7×(C67⋊C3)⋊C11
unambiguous semidirect product(D7×C67⋊C3)⋊C11

Splittings

Fitting, socle, derived, HallC7×C67 ⋊ C2×C3×C11
HallC7×(C67⋊C3)⋊C11 ⋊ C2
HallD7×C67⋊C11 ⋊ C3
HallC7×C67⋊C11 ⋊ C2×C3
HallD7×C67⋊C3 ⋊ C11
HallC7×C67⋊C3 ⋊ C2×C11
HallD7×C67 ⋊ C3×C11
HallC67⋊C11 ⋊ C3×D7
HallC67⋊C3 ⋊ C11×D7
SylowC67 ⋊ C3×C11×D7
SylowC7 ⋊ C2×(C67⋊C3)⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C67C2×C3×C11
LCSG ▷ C7×C67
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 469

Conjugacy classes & character table

175 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 65);