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C7×C11×D67⋊C3 #44526252

order30954
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×D67⋊C3
unambiguous semidirect product(C11×D67)⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C11×C67 ⋊ C2×C3
derived, SylowC67 ⋊ C2×C3×C7×C11
HallC7×C11×C67⋊C3 ⋊ C2
HallC7×C11×D67 ⋊ C3
HallC11×C67⋊C3 ⋊ C2×C7
HallC11×D67 ⋊ C3×C7
HallC7×C67⋊C3 ⋊ C2×C11
HallC7×D67 ⋊ C3×C11
HallC11×C67 ⋊ C2×C3×C7
HallC7×C67 ⋊ C2×C3×C11
HallC67⋊C3 ⋊ C2×C7×C11
HallD67 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC7×C11D67⋊C3
commutator, cosocle, hypocenterC67C2×C3×C7×C11
FrattiniC1G
Fitting, socleC7×C11×C67C2×C3
LCSG ▷ C67
UCSC1 ◁ C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5159

Conjugacy classes & character table

1309 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 33);