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C3×C17×Dic169 #46828126

order34476
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×Dic169

Splittings

derived, SylowC169 ⋊ C3×C4×C17
HallC3×C17×C169 ⋊ C4
HallC17×C169 ⋊ C3×C4
HallC3×C169 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D169
commutator, hypocenterC169C3×C4×C17
FrattiniC2×C13C3×C17×D13
FittingC2×C3×C17×C169C2
socle, prime radicalC2×C3×C13×C17D13
cosocleC2×C169C2×C3×C17
LCSG ▷ C169
UCSC1 ◁ C2×C3×C17

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34476

Conjugacy classes & character table

8772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34476, 7);