Finite Group Databasebeta

← Prev (#36348457) Next (#36348459) →

C2×C25×D221 #36348458

order22100
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C25×D221
unambiguous semidirect product(C2×C13)⋊(C25×D17)
unambiguous semidirect product(C2×C17)⋊(C25×D13)

Splittings

FittingC2×C13×C17×C25 ⋊ C2
derived, HallC13×C17 ⋊ C22×C25
HallC13×C17×C25 ⋊ C22
HallC17×C25 ⋊ C2×D13
HallC13×C25 ⋊ C2×D17
SylowC17 ⋊ C2×C25×D13
SylowC13 ⋊ C2×C25×D17

Subgroups

subgroupG/H
center, hypercenterC2×C25D221
commutator, hypocenterC13×C17C22×C25
FrattiniC5C2×C5×D221
FittingC2×C13×C17×C25C2
socleC2×C5×C13×C17C2×C5
prime radicalC2×C5×D221C5
cosocleC5×C13×C17C22×C5
LCSG ▷ C13×C17
UCSC1 ◁ C2×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11050

Conjugacy classes & character table

5600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22100, 49);