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C2×(C11⋊C5)⋊C8 #11724844

order880
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2

Aliases

direct productC2×(C11⋊C5)⋊C8
unambiguous semidirect product(C2×C11⋊C5)⋊C8
unambiguous semidirect product(C2×C11⋊C8)⋊C5

Splittings

derived, SylowC11 ⋊ C2×C5×C8
HallC2×C11⋊C8 ⋊ C5
HallC11⋊C5 ⋊ C2×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4AGL(1,𝔽11)
commutator, hypocenterC11C2×C5×C8
FrattiniC4C2×AGL(1,𝔽11)
FittingC2×C4×C11C2×C5
socleC22×C11C4×C5
prime radicalC22×C11⋊C5C4
cosocleC4×C11C22×C5
LCSG ▷ C11
UCSC1 ◁ C2×C4

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×(C11⋊C5)⋊C8, #66867⋊C5, C4⋊((C11⋊C5)⋊C8), …
maximal normal subgroup ofC4×(C11⋊C5)⋊C8, #66867⋊C5, C4⋊((C11⋊C5)⋊C8), …
maximal quotient ofC4×(C11⋊C5)⋊C8, C4⋊((C11⋊C5)⋊C8), C2×(C11⋊C5)⋊C16, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 12);