Finite Group Databasebeta

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C32×C5×C19×Dic11 #49178500

order37620
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C19 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C19×Dic11

Splittings

derived, SylowC11 ⋊ C32×C4×C5×C19
HallC32×C5×C11×C19 ⋊ C4
HallC32×C11×C19 ⋊ C4×C5
HallC5×C11×C19 ⋊ C32×C4
HallC32×C5×C11 ⋊ C4×C19
HallC11×C19 ⋊ C32×C4×C5
HallC32×C11 ⋊ C4×C5×C19
HallC5×C11 ⋊ C32×C4×C19

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5×C19D11
commutator, hypocenterC11C32×C4×C5×C19
FrattiniC2C32×C5×C19×D11
Fitting, socle, prime radicalC2×C32×C5×C11×C19C2
cosocleC2×C11C2×C32×C5×C19
LCSG ▷ C11
UCSC1 ◁ C2×C32×C5×C19

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

11970 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 209);