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Q8×C11×AGL(1,𝔽5) #13183340

order1760
automorphism?
homologyAbelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22

Aliases

direct productQ8×C11×AGL(1,𝔽5)

Splittings

FittingC5×Q8×C11 ⋊ C4
HallC5×C11 ⋊ C4×Q8
SylowC5 ⋊ C4×Q8×C11

Subgroups

subgroupG/H
centerC2×C11C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C11
FrattiniC2C22×C11×AGL(1,𝔽5)
FittingC5×Q8×C11C4
socleC2×C5×C11C22×C4
prime radicalC2×D5×C11C23
cosocleC2×D5C23×C11
hypercenterQ8×C11AGL(1,𝔽5)
hypocenterC5C4×Q8×C11
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ Q8×C11

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 440

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1149);