Finite Group Databasebeta

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D3×C7×C11×C37 #30685305

order17094
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C2×C7×C11×C37 · Schur multiplier (H2) = C1

Aliases

direct productD3×C7×C11×C37
unambiguous semidirect productC3⋊(C2×C7×C11×C37)

Splittings

Fitting, socle, HallC3×C7×C11×C37 ⋊ C2
derived, SylowC3 ⋊ C2×C7×C11×C37
HallC3×C11×C37 ⋊ C2×C7
HallC3×C7×C37 ⋊ C2×C11
HallC3×C7×C11 ⋊ C2×C37
HallC3×C37 ⋊ C2×C7×C11
HallC3×C11 ⋊ C2×C7×C37
HallC3×C7 ⋊ C2×C11×C37

Subgroups

subgroupG/H
center, hypercenterC7×C11×C37D3
commutator, cosocle, hypocenterC3C2×C7×C11×C37
FrattiniC1G
Fitting, socleC3×C7×C11×C37C2
LCSG ▷ C3
UCSC1 ◁ C7×C11×C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8547

Conjugacy classes & character table

8547 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C7×C11×D37, D3×C7×D11×C37, D3×C7×D407, …
maximal normal subgroup ofD3×C7×C11×D37, D3×C7×D11×C37, D3×C7×D407, …
maximal quotient ofC7×C11×Dic3×C37, C2×D3×C7×C11×C37

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17094, 13);