Finite Group Databasebeta

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C22×C5×C11×#4294 #49178414

order37620
automorphism?
homologyAbelianization (H1) = C22×C5×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C11×#4294

Splittings

derived, SylowC19 ⋊ C22×C5×C9×C11
HallC22×C5×C11×C19 ⋊ C9
HallC5×C11×C19 ⋊ C22×C9
HallC22×C11×C19 ⋊ C5×C9
HallC22×C5×C19 ⋊ C9×C11
HallC11×C19 ⋊ C22×C5×C9
HallC5×C19 ⋊ C22×C9×C11
HallC22×C19 ⋊ C5×C9×C11

Subgroups

subgroupG/H
center, hypercenterC22×C3×C5×C11C19⋊C3
commutator, hypocenterC19C22×C5×C9×C11
FrattiniC3C22×C5×C11×C19⋊C3
Fitting, socle, prime radicalC22×C3×C5×C11×C19C3
cosocleC3×C19C22×C3×C5×C11
LCSG ▷ C19
UCSC1 ◁ C22×C3×C5×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37620

Conjugacy classes & character table

5940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 123);