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C23×(C7⋊C9)⋊AGL(1,𝔽5) #44394358

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

Aliases

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

Splittings

derived, HallC5×C7 ⋊ C4×C9×C23
HallC5×C23×C7⋊C9 ⋊ C4
HallC23×C7⋊AGL(1,𝔽5) ⋊ C9
HallC23×C7⋊C9 ⋊ AGL(1,𝔽5)
HallC5×C7×C23 ⋊ C4×C9
HallC5×C7⋊C9 ⋊ C4×C23
HallC7×C23 ⋊ C9×AGL(1,𝔽5)
HallC7⋊AGL(1,𝔽5) ⋊ C9×C23
HallC5×C23 ⋊ Dic7⋊C9
HallC7⋊C9 ⋊ AGL(1,𝔽5)×C23
SylowC7 ⋊ C9×AGL(1,𝔽5)×C23
SylowC5 ⋊ C23×Dic7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C23ΓL(1,𝔽8)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C9×C23
FrattiniC3C23×ΓL(1,𝔽8)⋊AGL(1,𝔽5)
Fitting, socleC3×C5×C7×C23C3×C4
prime radicalC3×C7×D5×C23C2×C3
cosocleC3×C7×D5C2×C3×C23
LCSG ▷ C5×C7
UCSC1 ◁ C3×C23

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7245

Conjugacy classes & character table

1311 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 27);