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C9×C23×C7⋊AGL(1,𝔽5) #44394378

order28980
automorphism?
homologyAbelianization (H1) = C4×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC9×C23×C7⋊AGL(1,𝔽5)

Splittings

Fitting, HallC5×C7×C9×C23 ⋊ C4
derived, HallC5×C7 ⋊ C4×C9×C23
HallC7×C9×C23 ⋊ AGL(1,𝔽5)
HallC5×C9×C23 ⋊ Dic7
HallC5×C7×C23 ⋊ C4×C9
HallC5×C7×C9 ⋊ C4×C23
HallC7×C23 ⋊ C9×AGL(1,𝔽5)
HallC5×C23 ⋊ C9×Dic7
HallC7×C9 ⋊ AGL(1,𝔽5)×C23
HallC5×C9 ⋊ C23×Dic7
SylowC7 ⋊ C9×AGL(1,𝔽5)×C23
SylowC5 ⋊ C9×C23×Dic7

Subgroups

subgroupG/H
center, hypercenterC9×C23C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C9×C23
FrattiniC3C3×C23×C7⋊AGL(1,𝔽5)
FittingC5×C7×C9×C23C4
socleC3×C5×C7×C23C3×C4
prime radicalC3×C7×D5×C23C2×C3
cosocleC3×C7×D5C2×C3×C23
LCSG ▷ C5×C7
UCSC1 ◁ C9×C23

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7245

Conjugacy classes & character table

3519 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 47);