Finite Group Databasebeta

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C5×C13×C3⋊(C3⋊#261) #44478295

order30420
automorphism?
homologyAbelianization (H1) = C4×C5×C13 · Schur multiplier (H2) = C3

Aliases

direct productC5×C13×C3⋊(C3⋊#261)
unambiguous semidirect productC3⋊(C5×C13×C3⋊#261)

Splittings

Fitting, socle, HallC32×C5×C132 ⋊ C4
derivedC32×C13 ⋊ C4×C5×C13
HallC32×C132 ⋊ C4×C5
HallC5×C132 ⋊ C3⋊Dic3
SylowC132 ⋊ C5×C3⋊Dic3
HallC32×C5 ⋊ C13×#261
SylowC32 ⋊ C5×C13×#261

Subgroups

subgroupG/H
center, hypercenterC5×C13C3⋊(C3⋊#261)
commutator, hypocenterC32×C13C4×C5×C13
FrattiniC1G
Fitting, socleC32×C5×C132C4
prime radicalC32×C5×C13×D13C2
cosocleC32×D13C2×C5×C13
LCSG ▷ C32×C13
UCSC1 ◁ C5×C13

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2340

Conjugacy classes & character table

2535 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 884);