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C169×C9⋊AGL(1,𝔽5) #44477442

order30420
automorphism?
homologyAbelianization (H1) = C4×C169 · Schur multiplier (H2) = C1

Aliases

direct productC169×C9⋊AGL(1,𝔽5)
unambiguous semidirect productC9⋊(AGL(1,𝔽5)×C169)

Splittings

Fitting, HallC5×C9×C169 ⋊ C4
derived, HallC5×C9 ⋊ C4×C169
HallC9×C169 ⋊ AGL(1,𝔽5)
HallC5×C169 ⋊ Dic9
SylowC9 ⋊ AGL(1,𝔽5)×C169
SylowC5 ⋊ Dic9×C169

Subgroups

subgroupG/H
center, hypercenterC169C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C169
FrattiniC3×C13C13×ΓL(1,𝔽16)
FittingC5×C9×C169C4
socleC3×C5×C13Dic3×C13
prime radicalC3×D5×C13D3×C13
cosocleC9×D5×C13C2×C13
LCSG ▷ C5×C9
UCSC1 ◁ C169

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7605

Conjugacy classes & character table

3549 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 31);