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C11×ΓL(1,𝔽8)⋊#1039 #37528359

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×ΓL(1,𝔽8)⋊#1039
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×#1039)

Splittings

derived, HallC52×C7 ⋊ C3×C4×C11
HallC11×C7⋊#1039 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C4
HallC52×C7×C11 ⋊ C3×C4
HallC7⋊#1039 ⋊ C3×C11
HallC52×ΓL(1,𝔽8) ⋊ C4×C11
HallC52×C11 ⋊ ΓL(1,𝔽8)⋊C4
HallC11×ΓL(1,𝔽8) ⋊ #1039
HallC7×C11 ⋊ C3×#1039
SylowC52 ⋊ C11×ΓL(1,𝔽8)⋊C4
HallΓL(1,𝔽8) ⋊ C11×#1039
SylowC7 ⋊ C3×C11×#1039

Subgroups

subgroupG/H
center, hypercenterC2×C11C5⋊(C5⋊AGL(1,𝔽7))
commutator, hypocenterC52×C7C3×C4×C11
FrattiniC2C11×C5⋊(C5⋊AGL(1,𝔽7))
Fitting, socleC2×C52×C7×C11C2×C3
prime radicalC2×C52×C11×ΓL(1,𝔽8)C2
cosocleC2×C52×C7C2×C3×C11
LCSG ▷ C52×C7
UCSC1 ◁ C2×C11

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

1474 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 170);