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C7×C59×ΓL(1,𝔽16) #37613399

order24780
automorphism?
homologyAbelianization (H1) = C4×C7×C59 · Schur multiplier (H2) = C1

Aliases

direct productC7×C59×ΓL(1,𝔽16)
unambiguous semidirect productC3⋊(C7×AGL(1,𝔽5)×C59)

Splittings

Fitting, socle, HallC3×C5×C7×C59 ⋊ C4
derived, HallC3×C5 ⋊ C4×C7×C59
HallC5×C7×C59 ⋊ Dic3
HallC3×C7×C59 ⋊ AGL(1,𝔽5)
HallC3×C5×C59 ⋊ C4×C7
HallC5×C59 ⋊ C7×Dic3
HallC3×C59 ⋊ C7×AGL(1,𝔽5)
HallC3×C5×C7 ⋊ C4×C59
HallC5×C7 ⋊ Dic3×C59
HallC3×C7 ⋊ AGL(1,𝔽5)×C59
SylowC5 ⋊ C7×Dic3×C59
SylowC3 ⋊ C7×AGL(1,𝔽5)×C59

Subgroups

subgroupG/H
center, hypercenterC7×C59ΓL(1,𝔽16)
commutator, hypocenterC3×C5C4×C7×C59
FrattiniC1G
Fitting, socleC3×C5×C7×C59C4
prime radicalC3×C7×D5×C59C2
cosocleC3×D5C2×C7×C59
LCSG ▷ C3×C5
UCSC1 ◁ C7×C59

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6195

Conjugacy classes & character table

3717 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24780, 61);