Finite Group Databasebeta

← Prev (#46828127) Next (#46828129) →

Dic3×C17×C169 #46828128

order34476
automorphism?
homologyAbelianization (H1) = C4×C17×C169 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C17×C169
unambiguous semidirect productC3⋊(C4×C17×C169)

Splittings

derived, SylowC3 ⋊ C4×C17×C169
HallC3×C17×C169 ⋊ C4
HallC3×C169 ⋊ C4×C17
HallC3×C17 ⋊ C4×C169

Subgroups

subgroupG/H
center, hypercenterC2×C17×C169D3
commutator, hypocenterC3C4×C17×C169
FrattiniC2×C13D3×C13×C17
FittingC2×C3×C17×C169C2
socle, prime radicalC2×C3×C13×C17C2×C13
cosocleC2×C3×C13C2×C13×C17
LCSG ▷ C3
UCSC1 ◁ C2×C17×C169

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34476

Conjugacy classes & character table

17238 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34476, 9);