Finite Group Databasebeta

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C2×(C103⋊C9)⋊C17 #44538536

order31518
automorphism?
homologyAbelianization (H1) = C2×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×(C103⋊C9)⋊C17
unambiguous semidirect product(C2×C103⋊C9)⋊C17
unambiguous semidirect product(C2×C103⋊C17)⋊C9

Splittings

derived, SylowC103 ⋊ C2×C9×C17
HallC2×C103⋊C17 ⋊ C9
HallC2×C103⋊C9 ⋊ C17
HallC103⋊C17 ⋊ C2×C9
HallC103⋊C9 ⋊ C2×C17
HallC2×C103 ⋊ C9×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3(C103⋊C3)⋊C17
commutator, hypocenterC103C2×C9×C17
FrattiniC3C2×(C103⋊C3)⋊C17
Fitting, socleC2×C3×C103C3×C17
prime radicalC2×C3×C103⋊C17C3
cosocleC3×C103C2×C3×C17
LCSG ▷ C103
UCSC1 ◁ C2×C3

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1854

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31518, 4);