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C5×C361⋊AGL(1,𝔽5) #49115459

order36100
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C361⋊AGL(1,𝔽5)
unambiguous semidirect productC361⋊(C5×AGL(1,𝔽5))

Splittings

Fitting, HallC52×C361 ⋊ C4
derivedC5×C361 ⋊ C4×C5
SylowC361 ⋊ C5×AGL(1,𝔽5)
SylowC52 ⋊ Dic361

Subgroups

subgroupG/H
center, hypercenterC5C361⋊AGL(1,𝔽5)
commutator, hypocenterC5×C361C4×C5
FrattiniC19C5×C19⋊AGL(1,𝔽5)
FittingC52×C361C4
socleC52×C19Dic19
prime radicalC5×D5×C19D19
cosocleD5×C361C2×C5
LCSG ▷ C5×C361
UCSC1 ◁ C5

39 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7220

Conjugacy classes & character table

3625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36100, 20);