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C3×C7⋊(D67⋊C11) #44526247

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

Aliases

direct productC3×C7⋊(D67⋊C11)
unambiguous semidirect product(C3×D469)⋊C11

Splittings

Fitting, socle, HallC3×C7×C67 ⋊ C2×C11
derived, HallC7×C67 ⋊ C2×C3×C11
HallC3×C7×C67⋊C11 ⋊ C2
HallC7×C67⋊C11 ⋊ C2×C3
HallC3×D469 ⋊ C11
HallC3×C67⋊C11 ⋊ D7
HallD469 ⋊ C3×C11
HallC67⋊C11 ⋊ C3×D7
HallC3×C67 ⋊ C11×D7
SylowC67 ⋊ C3×C11×D7
HallC3×C7 ⋊ D67⋊C11
SylowC7 ⋊ C3×D67⋊C11

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(D67⋊C11)
commutator, cosocle, hypocenterC7×C67C2×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C67C2×C11
LCSG ▷ C7×C67
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1407

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 28);