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C7×C9×C23⋊AGL(1,𝔽5) #44394377

order28980
automorphism?
homologyAbelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×C23⋊AGL(1,𝔽5)
unambiguous semidirect productC23⋊(C7×C9×AGL(1,𝔽5))

Splittings

Fitting, HallC5×C7×C9×C23 ⋊ C4
derived, HallC5×C23 ⋊ C4×C7×C9
HallC7×C9×C23 ⋊ AGL(1,𝔽5)
HallC5×C9×C23 ⋊ C4×C7
HallC5×C7×C23 ⋊ C4×C9
HallC5×C7×C9 ⋊ Dic23
HallC9×C23 ⋊ C7×AGL(1,𝔽5)
HallC7×C23 ⋊ C9×AGL(1,𝔽5)
HallC5×C9 ⋊ C7×Dic23
HallC5×C7 ⋊ C9×Dic23
SylowC23 ⋊ C7×C9×AGL(1,𝔽5)
SylowC5 ⋊ C7×C9×Dic23

Subgroups

subgroupG/H
center, hypercenterC7×C9C23⋊AGL(1,𝔽5)
commutator, hypocenterC5×C23C4×C7×C9
FrattiniC3C3×C7×C23⋊AGL(1,𝔽5)
FittingC5×C7×C9×C23C4
socleC3×C5×C7×C23C3×C4
prime radicalC3×C7×D5×C23C2×C3
cosocleC3×D5×C23C2×C3×C7
LCSG ▷ C5×C23
UCSC1 ◁ C7×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7245

Conjugacy classes & character table

3087 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 46);