Finite Group Databasebeta

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C7×C17×D37⋊C3 #40996111

order26418
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C17×D37⋊C3
unambiguous semidirect productD37⋊(C3×C7×C17)
unambiguous semidirect product(C37⋊C3)⋊(C2×C7×C17)
unambiguous semidirect product(C17×D37)⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C17×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C2×C3×C7×C17
HallC7×C17×C37⋊C3 ⋊ C2
HallC7×C17×D37 ⋊ C3
HallC17×C37⋊C3 ⋊ C2×C7
HallC17×D37 ⋊ C3×C7
HallC7×C37⋊C3 ⋊ C2×C17
HallC17×C37 ⋊ C2×C3×C7
HallC7×D37 ⋊ C3×C17
HallC7×C37 ⋊ C2×C3×C17
HallC37⋊C3 ⋊ C2×C7×C17
HallD37 ⋊ C3×C7×C17

Subgroups

subgroupG/H
center, hypercenterC7×C17D37⋊C3
commutator, cosocle, hypocenterC37C2×C3×C7×C17
FrattiniC1G
Fitting, socleC7×C17×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C7×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4403

Conjugacy classes & character table

1428 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26418, 21);