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C2×C3×C25×D119 #49087652

order35700
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C25×D119
unambiguous semidirect product(C2×C17)⋊(C3×D7×C25)

Splittings

FittingC2×C3×C7×C17×C25 ⋊ C2
derived, HallC7×C17 ⋊ C22×C3×C25
HallC3×C7×C17×C25 ⋊ C22
HallC7×C17×C25 ⋊ C22×C3
HallC3×C17×C25 ⋊ C2×D7
HallC3×C7×C25 ⋊ C2×D17
HallC17×C25 ⋊ C2×C3×D7
HallC3×C7×C17 ⋊ C22×C25
HallC7×C25 ⋊ C2×C3×D17
HallC3×C17 ⋊ C2×D7×C25
HallC3×C7 ⋊ C2×C25×D17
SylowC17 ⋊ C2×C3×D7×C25
SylowC7 ⋊ C2×C3×C25×D17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D119
commutator, hypocenterC7×C17C22×C3×C25
FrattiniC5C2×C3×C5×D119
FittingC2×C3×C7×C17×C25C2
socleC2×C3×C5×C7×C17C2×C5
prime radicalC2×C3×C5×D119C5
cosocleC5×C7×C17C22×C3×C5
LCSG ▷ C7×C17
UCSC1 ◁ C2×C3×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17850

Conjugacy classes & character table

9150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35700, 126);