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C2×Q8×C11⋊C5 #11724965

order880
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC2×Q8×C11⋊C5
unambiguous semidirect product(C2×Q8×C11)⋊C5

Splittings

Fitting, HallC2×Q8×C11 ⋊ C5
SylowC11 ⋊ C2×C5×Q8

Subgroups

subgroupG/H
centerC22C22×C11⋊C5
commutator, cosocleC2×C11C23×C5
FrattiniC2C23×C11⋊C5
FittingC2×Q8×C11C5
socleC22×C11C22×C5
prime radicalC22×C11⋊C5C22
hypercenterC2×Q8C11⋊C5
hypocenterC11C2×C5×Q8
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×Q8

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 21
transitive degreeμt(G) = 176

A minimal faithful permutation representation — 3 generators on 21 points:

(1,2)(12,13,15,18,17)(14,16,20,21,19);(3,4,5,6)(7,10,9,8)(11,12,14,17,13,15,19,21,16,18,20);(3,7,5,9)(4,8,6,10)

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#66899⋊C5, #66900⋊C5, #101×C11⋊C5, …
maximal normal subgroup of#66899⋊C5, #66900⋊C5, #101×C11⋊C5, …
maximal quotient ofC2×C4⋊C4×C11⋊C5, C4×Q8×C11⋊C5, C22⋊Q8×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 133);