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C17×ΓL(1,𝔽8)×Dic17 #37566196

order24276
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×ΓL(1,𝔽8)×Dic17
unambiguous semidirect product(C7×Dic17)⋊(C3×C17)
unambiguous semidirect product(C7×C17×Dic17)⋊C3

Splittings

derivedC7×C17 ⋊ C3×C4×C17
HallC7×C17×Dic17 ⋊ C3
HallC172×ΓL(1,𝔽8) ⋊ C4
HallC7×C172 ⋊ C3×C4
SylowC172 ⋊ C4×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C17×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C17ΓL(1,𝔽8)×D17
commutator, hypocenterC7×C17C3×C4×C17
FrattiniC2C17×ΓL(1,𝔽8)×D17
Fitting, socleC2×C7×C172C2×C3
prime radicalC2×C172×ΓL(1,𝔽8)C2
cosocleC2×C7×C17C2×C3×C17
LCSG ▷ C7×C17
UCSC1 ◁ C2×C17

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 476

Conjugacy classes & character table

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24276, 49);