Finite Group Databasebeta

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C11×D17×C7⋊C9 #37555624

order23562
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D17×C7⋊C9
unambiguous semidirect productC17⋊(C2×C11×C7⋊C9)
unambiguous semidirect product(C7×D17)⋊(C9×C11)
unambiguous semidirect product(C7×C11×D17)⋊C9

Splittings

derived, HallC7×C17 ⋊ C2×C9×C11
HallC11×C17×C7⋊C9 ⋊ C2
HallC7×C11×D17 ⋊ C9
HallC7×C11×C17 ⋊ C2×C9
HallC17×C7⋊C9 ⋊ C2×C11
HallC7×D17 ⋊ C9×C11
HallC11×C17 ⋊ C2×C7⋊C9
HallC7×C11 ⋊ C9×D17
SylowC17 ⋊ C2×C11×C7⋊C9
SylowC7 ⋊ C9×C11×D17

Subgroups

subgroupG/H
center, hypercenterC3×C11ΓL(1,𝔽8)×D17
commutator, hypocenterC7×C17C2×C9×C11
FrattiniC3C11×ΓL(1,𝔽8)×D17
Fitting, socleC3×C7×C11×C17C2×C3
prime radicalC3×C7×C11×D17C3
cosocleC3×C7×C17C2×C3×C11
LCSG ▷ C7×C17
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11781

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23562, 18);