Finite Group Databasebeta

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C5×C9×C13×Dic13 #44477600

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

Aliases

direct productC5×C9×C13×Dic13

Splittings

derivedC13 ⋊ C4×C5×C9×C13
HallC5×C9×C132 ⋊ C4
HallC9×C132 ⋊ C4×C5
HallC5×C132 ⋊ C4×C9
SylowC132 ⋊ C4×C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9×C13D13
commutator, hypocenterC13C4×C5×C9×C13
FrattiniC2×C3C3×C5×C13×D13
FittingC2×C5×C9×C132C2
socle, prime radicalC2×C3×C5×C132C2×C3
cosocleC2×C3×C13C2×C3×C5×C13
LCSG ▷ C13
UCSC1 ◁ C2×C5×C9×C13

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2340

Conjugacy classes & character table

9360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 189);