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C7×D15⋊D89 #49153204

order37380
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D15⋊D89
unambiguous semidirect productD15⋊(C7×D89)
unambiguous semidirect productD267⋊(C7×D5)
unambiguous semidirect productD445⋊(D3×C7)

Splittings

Fitting, socle, HallC3×C5×C7×C89 ⋊ C22
derived, HallC3×C5×C89 ⋊ C22×C7
HallC5×C7×C89 ⋊ C2×D3
HallC3×C7×C89 ⋊ C2×D5
HallC7×C89 ⋊ D3×D5
HallC5×C89 ⋊ C2×D3×C7
HallC3×C89 ⋊ C2×C7×D5
HallC3×C5×C7 ⋊ C2×D89
SylowC89 ⋊ D3×C7×D5
HallC5×C7 ⋊ D3×D89
HallC3×C7 ⋊ D5×D89
HallC3×C5 ⋊ C2×C7×D89
SylowC5 ⋊ D3×C7×D89
SylowC3 ⋊ C7×D5×D89

Subgroups

subgroupG/H
center, hypercenterC7D15⋊D89
commutator, cosocle, hypocenterC3×C5×C89C22×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C89C22
LCSG ▷ C3×C5×C89
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9345

Conjugacy classes & character table

2856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 98);