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C4×C25×#4294 #30685368

order17100
isoclinismisoclinic class of C19⋊C3
automorphism?
homologyAbelianization (H1) = C4×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC4×C25×#4294

Splittings

derived, SylowC19 ⋊ C4×C9×C25
HallC4×C19×C25 ⋊ C9
HallC19×C25 ⋊ C4×C9
HallC4×C19 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC3×C4×C25C19⋊C3
commutator, hypocenterC19C4×C9×C25
FrattiniC2×C3×C5C2×C5×C19⋊C3
FittingC3×C4×C19×C25C3
socle, prime radical, cosocleC2×C3×C5×C19C2×C3×C5
LCSG ▷ C19
UCSC1 ◁ C3×C4×C25

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17100

Conjugacy classes & character table

2700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 5);