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C2×D251⋊C5 #19097616

order5020
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×D251⋊C5
unambiguous semidirect productD251⋊(C2×C5)
unambiguous semidirect product(C2×D251)⋊C5
unambiguous semidirect product(C251⋊C5)⋊C22
unambiguous semidirect product(C2×C251⋊C5)⋊C2

Splittings

Fitting, socleC2×C251 ⋊ C2×C5
derived, SylowC251 ⋊ C22×C5
HallC251⋊C5 ⋊ C22
HallC2×D251 ⋊ C5

Subgroups

subgroupG/H
center, hypercenterC2D251⋊C5
commutator, hypocenterC251C22×C5
FrattiniC1G
Fitting, socleC2×C251C2×C5
LCSG ▷ C251
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D251⋊C5, C2×C3×D251⋊C5, C2×C3⋊(D251⋊C5), …
maximal normal subgroup ofC2×C3×D251⋊C5, C2×#20262474⋊C2, C2×C5×D251⋊C5, …
maximal quotient ofD3×D251⋊C5, C2×C3×D251⋊C5, C2×C3⋊(D251⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5020, 8);