Finite Group Databasebeta

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C2×C11×D5⋊C8 #13183331

order1760
isoclinismisoclinic class of AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C23

Aliases

direct productC2×C11×D5⋊C8
unambiguous semidirect productD5⋊(C2×C8×C11)

Splittings

derived, SylowC5 ⋊ C22×C8×C11
HallC5×C11 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4×C11AGL(1,𝔽5)
commutator, hypocenterC5C22×C8×C11
FrattiniC2C22×C11×AGL(1,𝔽5)
FittingC2×C4×C5×C11C4
socleC22×C5×C11C2×C4
prime radicalC22×D5×C11C4
cosocleDic5C23×C11
LCSG ▷ C5
UCSC1 ◁ C2×C4×C11

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 880

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1140);