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C107×C9⋊AGL(1,𝔽5) #34064083

order19260
automorphism?
homologyAbelianization (H1) = C4×C107 · Schur multiplier (H2) = C1

Aliases

direct productC107×C9⋊AGL(1,𝔽5)
unambiguous semidirect productC9⋊(AGL(1,𝔽5)×C107)

Splittings

Fitting, HallC5×C9×C107 ⋊ C4
derived, HallC5×C9 ⋊ C4×C107
HallC9×C107 ⋊ AGL(1,𝔽5)
HallC5×C107 ⋊ Dic9
SylowC9 ⋊ AGL(1,𝔽5)×C107
SylowC5 ⋊ Dic9×C107

Subgroups

subgroupG/H
center, hypercenterC107C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C107
FrattiniC3ΓL(1,𝔽16)×C107
FittingC5×C9×C107C4
socleC3×C5×C107Dic3
prime radicalC3×D5×C107D3
cosocleC9×D5C2×C107
LCSG ▷ C5×C9
UCSC1 ◁ C107

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4815

Conjugacy classes & character table

2247 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19260, 14);