Finite Group Databasebeta

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C7×Dic3×C13×C17 #32915418

order18564
automorphism?
homologyAbelianization (H1) = C4×C7×C13×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic3×C13×C17
unambiguous semidirect productC3⋊(C4×C7×C13×C17)

Splittings

derived, SylowC3 ⋊ C4×C7×C13×C17
HallC3×C7×C13×C17 ⋊ C4
HallC3×C13×C17 ⋊ C4×C7
HallC3×C7×C17 ⋊ C4×C13
HallC3×C7×C13 ⋊ C4×C17
HallC3×C17 ⋊ C4×C7×C13
HallC3×C13 ⋊ C4×C7×C17
HallC3×C7 ⋊ C4×C13×C17

Subgroups

subgroupG/H
center, hypercenterC2×C7×C13×C17D3
commutator, hypocenterC3C4×C7×C13×C17
FrattiniC2D3×C7×C13×C17
Fitting, socle, prime radicalC2×C3×C7×C13×C17C2
cosocleC2×C3C2×C7×C13×C17
LCSG ▷ C3
UCSC1 ◁ C2×C7×C13×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18564

Conjugacy classes & character table

9282 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 13);