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C2×C5⋊D5×C289 #43274654

order28900
automorphism?
homologyAbelianization (H1) = C22×C289 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5⋊D5×C289
unambiguous semidirect product(C2×C5)⋊(D5×C289)

Splittings

FittingC2×C52×C289 ⋊ C2
derived, SylowC52 ⋊ C22×C289
HallC52×C289 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C289C5⋊D5
commutator, hypocenterC52C22×C289
FrattiniC17C2×C17×C5⋊D5
FittingC2×C52×C289C2
socleC2×C52×C17C2×C17
prime radicalC2×C17×C5⋊D5C17
cosocleC52×C17C22×C17
LCSG ▷ C52
UCSC1 ◁ C2×C289

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14450

Conjugacy classes & character table

8092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28900, 49);