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C2×C5⋊(C5⋊(#4294⋊C2)) #30685562

order17100
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5⋊(C5⋊(#4294⋊C2))
unambiguous semidirect product(C2×C5)⋊(C5⋊(#4294⋊C2))
unambiguous semidirect product(C2×#4294)⋊(C5⋊D5)

Splittings

derived, HallC52×C19 ⋊ C22×C9
HallC52×#4294 ⋊ C22
HallC2×C5⋊D95 ⋊ C9
Hall#4294 ⋊ C2×C5⋊D5
SylowC52 ⋊ C2×#4294⋊C2
SylowC19 ⋊ C2×C9×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(C5⋊(D19⋊C3))
commutator, hypocenterC52×C19C22×C9
FrattiniC3C2×C5⋊(C5⋊(D19⋊C3))
Fitting, socleC2×C3×C52×C19C2×C3
prime radicalC2×C3×C5⋊D95C3
cosocleC3×C52×C19C22×C3
LCSG ▷ C52×C19
UCSC1 ◁ C2×C3

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8550

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 199);