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C13×ΓL(1,𝔽8)×Dic17 #32915427

order18564
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×ΓL(1,𝔽8)×Dic17
unambiguous semidirect product(C7×Dic17)⋊(C3×C13)

Splittings

derived, HallC7×C17 ⋊ C3×C4×C13
HallC7×C13×Dic17 ⋊ C3
HallC13×C17×ΓL(1,𝔽8) ⋊ C4
HallC7×C13×C17 ⋊ C3×C4
HallC7×Dic17 ⋊ C3×C13
HallC17×ΓL(1,𝔽8) ⋊ C4×C13
HallC13×C17 ⋊ C4×ΓL(1,𝔽8)
HallC7×C13 ⋊ C3×Dic17
SylowC17 ⋊ C4×C13×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C13×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C13ΓL(1,𝔽8)×D17
commutator, hypocenterC7×C17C3×C4×C13
FrattiniC2C13×ΓL(1,𝔽8)×D17
Fitting, socleC2×C7×C13×C17C2×C3
prime radicalC2×C13×C17×ΓL(1,𝔽8)C2
cosocleC2×C7×C17C2×C3×C13
LCSG ▷ C7×C17
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6188

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18564, 22);