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C2×C5×C9×D139 #38736218

order25020
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C9×D139

Splittings

FittingC2×C5×C9×C139 ⋊ C2
derived, SylowC139 ⋊ C22×C5×C9
HallC5×C9×C139 ⋊ C22
HallC9×C139 ⋊ C22×C5
HallC5×C139 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D139
commutator, hypocenterC139C22×C5×C9
FrattiniC3C2×C3×C5×D139
FittingC2×C5×C9×C139C2
socleC2×C3×C5×C139C2×C3
prime radicalC2×C3×C5×D139C3
cosocleC3×C139C22×C3×C5
LCSG ▷ C139
UCSC1 ◁ C2×C5×C9

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12510

Conjugacy classes & character table

6390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25020, 40);