Finite Group Databasebeta

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C2×D17×C11⋊C25 #34035134

order18700
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×D17×C11⋊C25
unambiguous semidirect productC17⋊(C22×C11⋊C25)
unambiguous semidirect product(C2×C17)⋊(C2×C11⋊C25)
unambiguous semidirect product(C2×C11×D17)⋊C25

Splittings

derived, HallC11×C17 ⋊ C22×C25
HallC17×C11⋊C25 ⋊ C22
HallC2×C11×D17 ⋊ C25
SylowC17 ⋊ C22×C11⋊C25
SylowC11 ⋊ C2×C25×D17

Subgroups

subgroupG/H
center, hypercenterC2×C5D17×C11⋊C5
commutator, hypocenterC11×C17C22×C25
FrattiniC5C2×D17×C11⋊C5
Fitting, socleC2×C5×C11×C17C2×C5
prime radicalC2×C5×C11×D17C5
cosocleC5×C11×C17C22×C5
LCSG ▷ C11×C17
UCSC1 ◁ C2×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9350

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 19);