Finite Group Databasebeta

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C5×C3⋊(C3⋊#11717961) #49147174

order36900
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C3⋊(C3⋊#11717961)
unambiguous semidirect productC3⋊(C5×C3⋊#11717961)

Splittings

Fitting, socle, HallC32×C52×C41 ⋊ C4
derivedC32×C5×C41 ⋊ C4×C5
HallC52×C41 ⋊ C3⋊Dic3
HallC32×C41 ⋊ C5×AGL(1,𝔽5)
HallC32×C52 ⋊ #4223
SylowC41 ⋊ C5×C3⋊ΓL(1,𝔽16)
SylowC52 ⋊ C3⋊(C3⋊#4223)
SylowC32 ⋊ C5×#11717961

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C3⋊#11717961)
commutator, hypocenterC32×C5×C41C4×C5
FrattiniC1G
Fitting, socleC32×C52×C41C4
prime radicalC32×C5×D205C2
cosocleC32×D205C2×C5
LCSG ▷ C32×C5×C41
UCSC1 ◁ C5

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7380

Conjugacy classes & character table

2355 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 575);