Finite Group Databasebeta

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C2×C5×C9×C13⋊D13 #44477795

order30420
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2×C13

Aliases

direct productC2×C5×C9×C13⋊D13

Splittings

FittingC2×C5×C9×C132 ⋊ C2
derived, SylowC132 ⋊ C22×C5×C9
HallC5×C9×C132 ⋊ C22
HallC9×C132 ⋊ C22×C5
HallC5×C132 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9C13⋊D13
commutator, hypocenterC132C22×C5×C9
FrattiniC3C2×C3×C5×C13⋊D13
FittingC2×C5×C9×C132C2
socleC2×C3×C5×C132C2×C3
prime radicalC2×C3×C5×C13⋊D13C3
cosocleC3×C132C22×C3×C5
LCSG ▷ C132
UCSC1 ◁ C2×C5×C9

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15210

Conjugacy classes & character table

7740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 384);