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C25×C22⋊#4294 #30685396

order17100
automorphism?
homologyAbelianization (H1) = C9×C25 · Schur multiplier (H2) = C2

Aliases

direct productC25×C22⋊#4294
unambiguous semidirect productC22⋊(C25×#4294)
unambiguous semidirect product(C22×C25)⋊#4294

Splittings

derived, HallC22×C19 ⋊ C9×C25
HallC22×C19×C25 ⋊ C9
HallC19×C25 ⋊ C22⋊C9
HallC22×C25 ⋊ #4294
SylowC19 ⋊ C25×C22⋊C9
SylowC22 ⋊ C25×#4294

Subgroups

subgroupG/H
center, hypercenterC3×C25C22⋊(C19⋊C3)
commutator, hypocenterC22×C19C9×C25
FrattiniC3×C5C5×C22⋊(C19⋊C3)
FittingC22×C3×C19×C25C3
socle, prime radical, cosocleC22×C3×C5×C19C3×C5
LCSG ▷ C22×C19
UCSC1 ◁ C3×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8550

Conjugacy classes & character table

2100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 33);