Finite Group Databasebeta

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C2×C17×C25×D17 #43274690

order28900
automorphism?
homologyAbelianization (H1) = C22×C17×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×C25×D17
unambiguous semidirect productC17⋊(C22×C17×C25)
unambiguous semidirect product(C2×C17)⋊(C2×C17×C25)

Splittings

FittingC2×C172×C25 ⋊ C2
derivedC17 ⋊ C22×C17×C25
HallC172×C25 ⋊ C22
SylowC172 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C17×C25D17
commutator, hypocenterC17C22×C17×C25
FrattiniC5C2×C5×C17×D17
FittingC2×C172×C25C2
socleC2×C5×C172C2×C5
prime radicalC2×C5×C17×D17C5
cosocleC5×C17C22×C5×C17
LCSG ▷ C17
UCSC1 ◁ C2×C17×C25

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1700

Conjugacy classes & character table

8500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28900, 85);