Finite Group Databasebeta

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C17×D11×C7⋊C9 #37555625

order23562
automorphism?
homologyAbelianization (H1) = C2×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×D11×C7⋊C9
unambiguous semidirect productC11⋊(C2×C17×C7⋊C9)
unambiguous semidirect product(C7×D11)⋊(C9×C17)
unambiguous semidirect product(C7×C17×D11)⋊C9

Splittings

derived, HallC7×C11 ⋊ C2×C9×C17
HallC11×C17×C7⋊C9 ⋊ C2
HallC7×C17×D11 ⋊ C9
HallC7×C11×C17 ⋊ C2×C9
HallC11×C7⋊C9 ⋊ C2×C17
HallC11×C17 ⋊ C2×C7⋊C9
HallC7×D11 ⋊ C9×C17
HallC7×C17 ⋊ C9×D11
SylowC11 ⋊ C2×C17×C7⋊C9
SylowC7 ⋊ C9×C17×D11

Subgroups

subgroupG/H
center, hypercenterC3×C17ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C2×C9×C17
FrattiniC3C17×ΓL(1,𝔽8)×D11
Fitting, socleC3×C7×C11×C17C2×C3
prime radicalC3×C7×C17×D11C3
cosocleC3×C7×C11C2×C3×C17
LCSG ▷ C7×C11
UCSC1 ◁ C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

1785 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 19);