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C4×C172×ΓL(1,𝔽8) #37566203

order24276
automorphism?
homologyAbelianization (H1) = C3×C4×C172 · Schur multiplier (H2) = C17

Aliases

direct productC4×C172×ΓL(1,𝔽8)
unambiguous semidirect product(C4×C7)⋊(C3×C172)
unambiguous semidirect product(C4×C7×C17)⋊(C3×C17)

Splittings

Fitting, HallC4×C7×C172 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C172
HallC7×C172 ⋊ C3×C4
HallC4×C7 ⋊ C3×C172

Subgroups

subgroupG/H
center, hypercenterC4×C172ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C172
FrattiniC2C2×C172×ΓL(1,𝔽8)
FittingC4×C7×C172C3
socleC2×C7×C172C2×C3
prime radicalC2×C172×ΓL(1,𝔽8)C2
cosocleC2×C7C2×C3×C172
LCSG ▷ C7
UCSC1 ◁ C4×C172

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8092

Conjugacy classes & character table

5780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24276, 56);