Finite Group Databasebeta

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C5×C3⋊(C3⋊#10625193) #45686477

order33300
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C3⋊(C3⋊#10625193)
unambiguous semidirect productC3⋊(C5×C3⋊#10625193)

Splittings

Fitting, socle, HallC32×C52×C37 ⋊ C4
derivedC32×C5×C37 ⋊ C4×C5
HallC52×C37 ⋊ C3⋊Dic3
HallC32×C37 ⋊ C5×AGL(1,𝔽5)
HallC32×C52 ⋊ Dic37
SylowC37 ⋊ C5×C3⋊ΓL(1,𝔽16)
SylowC52 ⋊ C3⋊Dic111
SylowC32 ⋊ C5×#10625193

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(C3⋊#10625193)
commutator, hypocenterC32×C5×C37C4×C5
FrattiniC1G
Fitting, socleC32×C52×C37C4
prime radicalC32×C5×D5×C37C2
cosocleC32×D5×C37C2×C5
LCSG ▷ C32×C5×C37
UCSC1 ◁ C5

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6660

Conjugacy classes & character table

3345 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 750);