Finite Group Databasebeta

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C5×Dic1881 #49178306

order37620
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic1881
unambiguous semidirect productC9⋊(C5×Dic209)
unambiguous semidirect productC19⋊(C5×Dic99)

Splittings

derived, HallC9×C11×C19 ⋊ C4×C5
HallC5×C9×C11×C19 ⋊ C4
HallC5×C11×C19 ⋊ Dic9
HallC5×C9×C19 ⋊ Dic11
HallC5×C9×C11 ⋊ Dic19
HallC11×C19 ⋊ C5×Dic9
HallC9×C19 ⋊ C5×Dic11
HallC9×C11 ⋊ C5×Dic19
HallC5×C19 ⋊ Dic99
HallC5×C11 ⋊ Dic171
HallC5×C9 ⋊ Dic209
SylowC19 ⋊ C5×Dic99
SylowC11 ⋊ C5×Dic171
SylowC9 ⋊ C5×Dic209

Subgroups

subgroupG/H
center, hypercenterC2×C5D1881
commutator, hypocenterC9×C11×C19C4×C5
FrattiniC2×C3C5×D627
FittingC2×C5×C9×C11×C19C2
socle, prime radicalC2×C3×C5×C11×C19D3
cosocleC2×C9×C11×C19C2×C5
LCSG ▷ C9×C11×C19
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

9420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 15);