Finite Group Databasebeta

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C4×C5×C13×C13⋊C9 #44477597

order30420
automorphism?
homologyAbelianization (H1) = C4×C5×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C13×C13⋊C9
unambiguous semidirect product(C4×C13)⋊(C5×C9×C13)
unambiguous semidirect product(C4×C5×C13)⋊(C9×C13)

Splittings

derivedC13 ⋊ C4×C5×C9×C13
HallC4×C5×C132 ⋊ C9
HallC5×C132 ⋊ C4×C9
HallC4×C132 ⋊ C5×C9
SylowC132 ⋊ C4×C5×C9

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5×C13C13⋊C3
commutator, hypocenterC13C4×C5×C9×C13
FrattiniC2×C3C2×C5×C13×C13⋊C3
FittingC3×C4×C5×C132C3
socle, prime radicalC2×C3×C5×C132C2×C3
cosocleC2×C3×C13C2×C3×C5×C13
LCSG ▷ C13
UCSC1 ◁ C3×C4×C5×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2340

Conjugacy classes & character table

5460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 186);