Finite Group Databasebeta

← Prev (#31773230) Next (#31773232) →

C3×C5×C17×Dic17 #31773231

order17340
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C17×Dic17

Splittings

derivedC17 ⋊ C3×C4×C5×C17
HallC3×C5×C172 ⋊ C4
HallC5×C172 ⋊ C3×C4
HallC3×C172 ⋊ C4×C5
SylowC172 ⋊ C3×C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C17D17
commutator, hypocenterC17C3×C4×C5×C17
FrattiniC2C3×C5×C17×D17
Fitting, socle, prime radicalC2×C3×C5×C172C2
cosocleC2×C17C2×C3×C5×C17
LCSG ▷ C17
UCSC1 ◁ C2×C3×C5×C17

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1020

Conjugacy classes & character table

5100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17340, 44);