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C17×C23×ΓL(1,𝔽8)⋊C4 #45659256

order32844
automorphism?
homologyAbelianization (H1) = C3×C4×C17×C23 · Schur multiplier (H2) = C1

Aliases

direct productC17×C23×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C17×C23)
unambiguous semidirect productDic7⋊(C3×C17×C23)
unambiguous semidirect product(C17×Dic7)⋊(C3×C23)
unambiguous semidirect product(C23×Dic7)⋊(C3×C17)
unambiguous semidirect product(C17×C23×Dic7)⋊C3

Splittings

derived, SylowC7 ⋊ C3×C4×C17×C23
HallC17×C23×Dic7 ⋊ C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C4
HallC7×C17×C23 ⋊ C3×C4
HallC23×Dic7 ⋊ C3×C17
HallΓL(1,𝔽8)×C23 ⋊ C4×C17
HallC17×Dic7 ⋊ C3×C23
HallC17×ΓL(1,𝔽8) ⋊ C4×C23
HallC7×C23 ⋊ C3×C4×C17
HallC7×C17 ⋊ C3×C4×C23
HallDic7 ⋊ C3×C17×C23
HallΓL(1,𝔽8) ⋊ C4×C17×C23

Subgroups

subgroupG/H
center, hypercenterC2×C17×C23AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C17×C23
FrattiniC2C17×C23×AGL(1,𝔽7)
Fitting, socleC2×C7×C17×C23C2×C3
prime radicalC2×C17×ΓL(1,𝔽8)×C23C2
cosocleC2×C7C2×C3×C17×C23
LCSG ▷ C7
UCSC1 ◁ C2×C17×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10948

Conjugacy classes & character table

5474 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 21);