Finite Group Databasebeta

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C7×C9×C13×D17 #42123789

order27846
automorphism?
homologyAbelianization (H1) = C2×C7×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×C13×D17
unambiguous semidirect productC17⋊(C2×C7×C9×C13)

Splittings

Fitting, HallC7×C9×C13×C17 ⋊ C2
derived, SylowC17 ⋊ C2×C7×C9×C13
HallC9×C13×C17 ⋊ C2×C7
HallC7×C13×C17 ⋊ C2×C9
HallC7×C9×C17 ⋊ C2×C13
HallC13×C17 ⋊ C2×C7×C9
HallC9×C17 ⋊ C2×C7×C13
HallC7×C17 ⋊ C2×C9×C13

Subgroups

subgroupG/H
center, hypercenterC7×C9×C13D17
commutator, hypocenterC17C2×C7×C9×C13
FrattiniC3C3×C7×C13×D17
FittingC7×C9×C13×C17C2
socleC3×C7×C13×C17C2×C3
prime radicalC3×C7×C13×D17C3
cosocleC3×C17C2×C3×C7×C13
LCSG ▷ C17
UCSC1 ◁ C7×C9×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13923

Conjugacy classes & character table

8190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27846, 6);