Finite Group Databasebeta

← Prev (#29505652) Next (#29505654) →

C32×C17×Dic25 #29505653

order15300
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C32×C4×C17 · Schur multiplier (H2) = C3

Aliases

direct productC32×C17×Dic25

Splittings

derived, SylowC25 ⋊ C32×C4×C17
HallC32×C17×C25 ⋊ C4
HallC17×C25 ⋊ C32×C4
HallC32×C25 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C32×C17D25
commutator, hypocenterC25C32×C4×C17
FrattiniC2×C5C32×D5×C17
FittingC2×C32×C17×C25C2
socle, prime radicalC2×C32×C5×C17D5
cosocleC2×C25C2×C32×C17
LCSG ▷ C25
UCSC1 ◁ C2×C32×C17

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15300

Conjugacy classes & character table

4284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15300, 39);