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Cayley diagram

Q8×C11⋊C5 #89161

order440
isoclinismisoclinic class of D4×C11⋊C5
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C1

Aliases

direct productQ8×C11⋊C5
unambiguous semidirect product(Q8×C11)⋊C5

Splittings

Fitting, HallQ8×C11 ⋊ C5
SylowC11 ⋊ C5×Q8

Subgroups

subgroupG/H
center, FrattiniC2C22×C11⋊C5
commutator, socle, cosocleC2×C11C22×C5
FittingQ8×C11C5
prime radicalC2×C11⋊C5C22
hypercenterQ8C11⋊C5
hypocenterC11C5×Q8
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ Q8

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 88

A minimal faithful permutation representation — 2 generators on 19 points:

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

Conjugacy classes & character table

35 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#4325⋊C5, #4326⋊C5, SD16×C11⋊C5, …
maximal normal subgroup of#4325⋊C5, #4326⋊C5, SD16×C11⋊C5, …
maximal quotient ofC4⋊C4×C11⋊C5, C2×Q8×C11⋊C5, Dic6×C11⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 14);