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C2×C5×D5×C289 #43274652

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

Aliases

direct productC2×C5×D5×C289
unambiguous semidirect productC5⋊(C22×C5×C289)
unambiguous semidirect product(C2×C5)⋊(C2×C5×C289)

Splittings

FittingC2×C52×C289 ⋊ C2
derivedC5 ⋊ C22×C5×C289
HallC52×C289 ⋊ C22
SylowC52 ⋊ C22×C289

Subgroups

subgroupG/H
center, hypercenterC2×C5×C289D5
commutator, hypocenterC5C22×C5×C289
FrattiniC17C2×C5×D5×C17
FittingC2×C52×C289C2
socleC2×C52×C17C2×C17
prime radicalC2×C5×D5×C17C17
cosocleC5×C17C22×C5×C17
LCSG ▷ C5
UCSC1 ◁ C2×C5×C289

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5780

Conjugacy classes & character table

11560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28900, 47);