Finite Group Databasebeta

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C2×C11⋊C5×#4294⋊C2 #49178332

order37620
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊C5×#4294⋊C2
unambiguous semidirect product#4294⋊(C22×C11⋊C5)
unambiguous semidirect product(C2×#4294)⋊(C2×C11⋊C5)
unambiguous semidirect product(C2×C11×#4294⋊C2)⋊C5

Splittings

derived, HallC11×C19 ⋊ C22×C5×C9
HallC11⋊C5×#4294 ⋊ C22
HallC2×C11×#4294⋊C2 ⋊ C5
HallC2×D19×C11⋊C5 ⋊ C9
HallC11×#4294 ⋊ C22×C5
HallC19×C11⋊C5 ⋊ C22×C9
HallC2×C11×D19 ⋊ C5×C9
Hall#4294 ⋊ C22×C11⋊C5
HallC2×D19 ⋊ C9×C11⋊C5
SylowC19 ⋊ C22×C9×C11⋊C5
SylowC11 ⋊ C2×C5×#4294⋊C2

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊C5×D19⋊C3
commutator, hypocenterC11×C19C22×C5×C9
FrattiniC3C2×C11⋊C5×D19⋊C3
Fitting, socleC2×C3×C11×C19C2×C3×C5
prime radicalC2×C3×D19×C11⋊C5C3
cosocleC3×C11×C19C22×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3762

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 41);