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C2×C5⋊(D139⋊C9) #38736196

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

Aliases

direct productC2×C5⋊(D139⋊C9)
unambiguous semidirect product(C2×C5)⋊(D139⋊C9)
unambiguous semidirect product(C2×C139⋊C9)⋊D5
unambiguous semidirect product(C2×D695)⋊C9

Splittings

derived, HallC5×C139 ⋊ C22×C9
HallC5×C139⋊C9 ⋊ C22
HallC2×D695 ⋊ C9
HallC139⋊C9 ⋊ C2×D5
SylowC139 ⋊ C2×C9×D5
SylowC5 ⋊ C2×D139⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D139⋊C3)
commutator, hypocenterC5×C139C22×C9
FrattiniC3C2×C5⋊(D139⋊C3)
Fitting, socleC2×C3×C5×C139C2×C3
prime radicalC2×C3×D695C3
cosocleC3×C5×C139C22×C3
LCSG ▷ C5×C139
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12510

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25020, 18);