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C5×Dic1353 #41028554

order27060
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic1353
unambiguous semidirect productC3⋊(C5×Dic451)

Splittings

derived, HallC3×C11×C41 ⋊ C4×C5
HallC3×C5×C11×C41 ⋊ C4
HallC5×C11×C41 ⋊ Dic3
HallC3×C5×C41 ⋊ Dic11
HallC11×C41 ⋊ C5×Dic3
HallC5×C41 ⋊ Dic33
HallC3×C5×C11 ⋊ Dic41
HallC3×C41 ⋊ C5×Dic11
HallC5×C11 ⋊ Dic123
SylowC41 ⋊ C5×Dic33
HallC3×C11 ⋊ C5×Dic41
HallC3×C5 ⋊ Dic451
SylowC11 ⋊ C5×Dic123
SylowC3 ⋊ C5×Dic451

Subgroups

subgroupG/H
center, hypercenterC2×C5D1353
commutator, hypocenterC3×C11×C41C4×C5
FrattiniC2C5×D1353
Fitting, socle, prime radicalC2×C3×C5×C11×C41C2
cosocleC2×C3×C11×C41C2×C5
LCSG ▷ C3×C11×C41
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 27060

Conjugacy classes & character table

6780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27060, 18);