Finite Group Databasebeta

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C5×C11×C19×C3⋊Dic3 #49178486

order37620
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C19 · Schur multiplier (H2) = C3

Aliases

direct productC5×C11×C19×C3⋊Dic3
unambiguous semidirect productC3⋊(C5×C11×Dic3×C19)

Splittings

derived, SylowC32 ⋊ C4×C5×C11×C19
HallC32×C5×C11×C19 ⋊ C4
HallC32×C11×C19 ⋊ C4×C5
HallC32×C5×C19 ⋊ C4×C11
HallC32×C5×C11 ⋊ C4×C19
HallC32×C19 ⋊ C4×C5×C11
HallC32×C11 ⋊ C4×C5×C19
HallC32×C5 ⋊ C4×C11×C19

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11×C19C3⋊D3
commutator, hypocenterC32C4×C5×C11×C19
FrattiniC2C5×C11×C3⋊D3×C19
Fitting, socle, prime radicalC2×C32×C5×C11×C19C2
cosocleC2×C32C2×C5×C11×C19
LCSG ▷ C32
UCSC1 ◁ C2×C5×C11×C19

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

12540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 195);