Finite Group Databasebeta

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C17×Dic441 #44472370

order29988
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×Dic441
unambiguous semidirect productC9⋊(C17×Dic49)
unambiguous semidirect productC49⋊(C17×Dic9)

Splittings

derived, HallC9×C49 ⋊ C4×C17
HallC9×C17×C49 ⋊ C4
HallC17×C49 ⋊ Dic9
HallC9×C17 ⋊ Dic49
SylowC49 ⋊ C17×Dic9
SylowC9 ⋊ C17×Dic49

Subgroups

subgroupG/H
center, hypercenterC2×C17D441
commutator, hypocenterC9×C49C4×C17
FrattiniC2×C3×C7C17×D21
FittingC2×C9×C17×C49C2
socle, prime radicalC2×C3×C7×C17D21
cosocleC2×C9×C49C2×C17
LCSG ▷ C9×C49
UCSC1 ◁ C2×C17

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29988

Conjugacy classes & character table

7548 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 11);