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C23×ΓL(1,𝔽8)⋊Dic17 #45659258

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

Aliases

direct productC23×ΓL(1,𝔽8)⋊Dic17
unambiguous semidirect productΓL(1,𝔽8)⋊(C23×Dic17)
unambiguous semidirect productDic119⋊(C3×C23)
unambiguous semidirect product(C23×Dic119)⋊C3

Splittings

derived, HallC7×C17 ⋊ C3×C4×C23
HallC23×Dic119 ⋊ C3
HallC17×ΓL(1,𝔽8)×C23 ⋊ C4
HallC7×C17×C23 ⋊ C3×C4
HallΓL(1,𝔽8)×C23 ⋊ Dic17
HallDic119 ⋊ C3×C23
HallC17×C23 ⋊ ΓL(1,𝔽8)⋊C4
HallC17×ΓL(1,𝔽8) ⋊ C4×C23
HallC7×C23 ⋊ C3×Dic17
HallΓL(1,𝔽8) ⋊ C23×Dic17
SylowC17 ⋊ C23×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C23×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C23C17⋊AGL(1,𝔽7)
commutator, hypocenterC7×C17C3×C4×C23
FrattiniC2C23×C17⋊AGL(1,𝔽7)
Fitting, socleC2×C7×C17×C23C2×C3
prime radicalC2×C17×ΓL(1,𝔽8)×C23C2
cosocleC2×C7×C17C2×C3×C23
LCSG ▷ C7×C17
UCSC1 ◁ C2×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10948

Conjugacy classes & character table

2162 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32844, 23);