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C2×D4×C11⋊C5 #11724964

order880
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×D4×C11⋊C5
unambiguous semidirect productC4⋊(C22×C11⋊C5)
unambiguous semidirect productC22⋊(C22×C11⋊C5)
unambiguous semidirect productC23⋊(C2×C11⋊C5)
unambiguous semidirect product(C2×D4×C11)⋊C5

Splittings

Fitting, HallC2×D4×C11 ⋊ C5
SylowC11 ⋊ C2×C5×D4

Subgroups

subgroupG/H
centerC22C22×C11⋊C5
commutator, cosocleC2×C11C23×C5
FrattiniC2C23×C11⋊C5
FittingC2×D4×C11C5
socleC22×C11C22×C5
hypercenterC2×D4C11⋊C5
hypocenterC11C2×C5×D4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×D4

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 17
transitive degreeμt(G) = 88

A minimal faithful permutation representation — 3 generators on 17 points:

(1,2)(8,9,11,14,13)(10,12,16,17,15);(3,4,5,6)(7,8,10,13,9,11,15,17,12,14,16);(4,6)

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#66898⋊C5, #66896⋊C5, #66897⋊C5, …
maximal normal subgroup of#66898⋊C5, #66896⋊C5, #66897⋊C5, …
maximal quotient ofC2×C22⋊C4×C11⋊C5, C2×C4⋊C4×C11⋊C5, C4×D4×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 132);