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C3×C25×D221 #45684123

order33150
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×D221
unambiguous semidirect productC17⋊(C3×C25×D13)

Splittings

Fitting, HallC3×C13×C17×C25 ⋊ C2
derived, HallC13×C17 ⋊ C2×C3×C25
HallC13×C17×C25 ⋊ C2×C3
HallC3×C17×C25 ⋊ D13
HallC3×C13×C25 ⋊ D17
HallC3×C13×C17 ⋊ C2×C25
HallC17×C25 ⋊ C3×D13
HallC13×C25 ⋊ C3×D17
HallC3×C17 ⋊ C25×D13
HallC3×C13 ⋊ C25×D17
SylowC17 ⋊ C3×C25×D13
SylowC13 ⋊ C3×C25×D17

Subgroups

subgroupG/H
center, hypercenterC3×C25D221
commutator, hypocenterC13×C17C2×C3×C25
FrattiniC5C3×C5×D221
FittingC3×C13×C17×C25C2
socleC3×C5×C13×C17C2×C5
prime radicalC3×C5×D221C5
cosocleC5×C13×C17C2×C3×C5
LCSG ▷ C13×C17
UCSC1 ◁ C3×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16575

Conjugacy classes & character table

8400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33150, 5);