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C7×C3⋊#13184067 #49153187

order37380
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊#13184067
unambiguous semidirect productC3⋊(C7×#13184067)

Splittings

Fitting, socle, HallC3×C5×C7×C89 ⋊ C4
derived, HallC3×C5×C89 ⋊ C4×C7
HallC5×C7×C89 ⋊ Dic3
HallC3×C7×C89 ⋊ AGL(1,𝔽5)
HallC7×C89 ⋊ ΓL(1,𝔽16)
HallC5×C89 ⋊ C7×Dic3
HallC3×C89 ⋊ C7×AGL(1,𝔽5)
HallC3×C5×C7 ⋊ #67063
SylowC89 ⋊ C7×ΓL(1,𝔽16)
HallC5×C7 ⋊ C3⋊#67063
HallC3×C7 ⋊ #13184067
HallC3×C5 ⋊ C7×#67063
SylowC5 ⋊ C7×C3⋊#67063
SylowC3 ⋊ C7×#13184067

Subgroups

subgroupG/H
center, hypercenterC7C3⋊#13184067
commutator, hypocenterC3×C5×C89C4×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C89C4
prime radicalC3×C7×D445C2
cosocleC3×D445C2×C7
LCSG ▷ C3×C5×C89
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9345

Conjugacy classes & character table

2373 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 81);