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C11×ΓL(1,𝔽8)⋊Dic17 #30628101

order15708
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)⋊Dic17
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×Dic17)
unambiguous semidirect productDic119⋊(C3×C11)
unambiguous semidirect product(C11×Dic119)⋊C3

Splittings

derived, HallC7×C17 ⋊ C3×C4×C11
HallC11×Dic119 ⋊ C3
HallC11×C17×ΓL(1,𝔽8) ⋊ C4
HallC7×C11×C17 ⋊ C3×C4
HallDic119 ⋊ C3×C11
HallC17×ΓL(1,𝔽8) ⋊ C4×C11
HallC11×ΓL(1,𝔽8) ⋊ Dic17
HallC11×C17 ⋊ ΓL(1,𝔽8)⋊C4
HallC7×C11 ⋊ C3×Dic17
HallΓL(1,𝔽8) ⋊ C11×Dic17
SylowC17 ⋊ C11×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C3×C11×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C11C17⋊AGL(1,𝔽7)
commutator, hypocenterC7×C17C3×C4×C11
FrattiniC2C11×C17⋊AGL(1,𝔽7)
Fitting, socleC2×C7×C11×C17C2×C3
prime radicalC2×C11×C17×ΓL(1,𝔽8)C2
cosocleC2×C7×C17C2×C3×C11
LCSG ▷ C7×C17
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5236

Conjugacy classes & character table

1034 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 22);