Finite Group Databasebeta

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C17×Dic7×C13⋊C3 #32915438

order18564
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×Dic7×C13⋊C3

Splittings

derived, HallC7×C13 ⋊ C3×C4×C17
HallC13×C17×Dic7 ⋊ C3
HallC7×C17×C13⋊C3 ⋊ C4
HallC7×C13×C17 ⋊ C3×C4
HallC13×Dic7 ⋊ C3×C17
HallC7×C13⋊C3 ⋊ C4×C17
HallC13×C17 ⋊ C3×Dic7
HallC7×C17 ⋊ C4×C13⋊C3
SylowC13 ⋊ C3×C17×Dic7
SylowC7 ⋊ C4×C17×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C17D7×C13⋊C3
commutator, hypocenterC7×C13C3×C4×C17
FrattiniC2D7×C17×C13⋊C3
Fitting, socleC2×C7×C13×C17C2×C3
prime radicalC2×C7×C17×C13⋊C3C2
cosocleC2×C7×C13C2×C3×C17
LCSG ▷ C7×C13
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6188

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 33);