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C22×C19⋊C3×C121 #42119933

order27588
automorphism?
homologyAbelianization (H1) = C22×C3×C121 · Schur multiplier (H2) = C2

Aliases

direct productC22×C19⋊C3×C121

Splittings

Fitting, HallC22×C19×C121 ⋊ C3
derived, SylowC19 ⋊ C22×C3×C121
HallC19×C121 ⋊ C22×C3
HallC22×C19 ⋊ C3×C121

Subgroups

subgroupG/H
center, hypercenterC22×C121C19⋊C3
commutator, hypocenterC19C22×C3×C121
FrattiniC11C22×C11×C19⋊C3
FittingC22×C19×C121C3
socleC22×C11×C19C3×C11
prime radicalC22×C11×C19⋊C3C11
cosocleC11×C19C22×C3×C11
LCSG ▷ C19
UCSC1 ◁ C22×C121

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9196

Conjugacy classes & character table

4356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 25);