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C5×C132×Dic9 #44477605

order30420
automorphism?
homologyAbelianization (H1) = C4×C5×C132 · Schur multiplier (H2) = C13

Aliases

direct productC5×C132×Dic9
unambiguous semidirect productC9⋊(C4×C5×C132)

Splittings

derived, SylowC9 ⋊ C4×C5×C132
HallC5×C9×C132 ⋊ C4
HallC9×C132 ⋊ C4×C5
HallC5×C9 ⋊ C4×C132

Subgroups

subgroupG/H
center, hypercenterC2×C5×C132D9
commutator, hypocenterC9C4×C5×C132
FrattiniC2×C3C5×D3×C132
FittingC2×C5×C9×C132C2
socle, prime radicalC2×C3×C5×C132D3
cosocleC2×C9C2×C5×C132
LCSG ▷ C9
UCSC1 ◁ C2×C5×C132

288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30420

Conjugacy classes & character table

10140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 194);