Finite Group Databasebeta

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C3×C7×C11×D17 #21463265

order7854
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11×D17
unambiguous semidirect productC17⋊(C2×C3×C7×C11)

Splittings

Fitting, socle, HallC3×C7×C11×C17 ⋊ C2
derived, SylowC17 ⋊ C2×C3×C7×C11
HallC7×C11×C17 ⋊ C2×C3
HallC3×C11×C17 ⋊ C2×C7
HallC3×C7×C17 ⋊ C2×C11
HallC11×C17 ⋊ C2×C3×C7
HallC7×C17 ⋊ C2×C3×C11
HallC3×C17 ⋊ C2×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11D17
commutator, hypocenterC17C2×C3×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C17C2
LCSG ▷ C17
UCSC1 ◁ C3×C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×C11×#595, C3×C7×C11⋊#595, C3×C7×D11×D17, …
maximal normal subgroup ofC3×C7×C11×#595, C3×C7×C11⋊#595, C3×C7×D11×D17, …
maximal quotient ofC3×C7×C11×Dic17, C2×C3×C7×C11×D17, C7×C9×C11×D17, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7854, 3);