Finite Group Databasebeta

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C17×Dic31⋊C9 #34039007

order18972
automorphism?
homologyAbelianization (H1) = C4×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×Dic31⋊C9
unambiguous semidirect productDic31⋊(C9×C17)
unambiguous semidirect product(C31⋊C9)⋊(C4×C17)
unambiguous semidirect product(C17×Dic31)⋊C9

Splittings

derived, SylowC31 ⋊ C4×C9×C17
HallC17×C31⋊C9 ⋊ C4
HallC17×Dic31 ⋊ C9
HallC17×C31 ⋊ C4×C9
HallC31⋊C9 ⋊ C4×C17
HallDic31 ⋊ C9×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D31⋊C3
commutator, hypocenterC31C4×C9×C17
FrattiniC2×C3C17×D31⋊C3
Fitting, socle, prime radicalC2×C3×C17×C31C2×C3
cosocleC2×C3×C31C2×C3×C17
LCSG ▷ C31
UCSC1 ◁ C2×C3×C17

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18972

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18972, 10);