Finite Group Databasebeta

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C11×#676 #11724907

order880
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#676

Splittings

FittingC5×C8×C11 ⋊ C2
HallC5×C11 ⋊ M16
SylowC5 ⋊ C11×M16

Subgroups

subgroupG/H
centerC4×C11C2×D5
commutatorC2×C5C2×C4×C11
FrattiniC4C2×D5×C11
FittingC5×C8×C11C2
socleC2×C5×C11C2×C4
prime radicalC2×D5×C11C4
cosocleC4×C5C22×C11
hypercenterC8×C11D5
hypocenterC5C11×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C11 ◁ C8×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 440

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,16,14)(17,18,19,22,20,21,23,24);(13,14)(15,16)(18,21)(22,24)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD11×#676, #13182663, #13182669, …
maximal normal subgroup ofD11×#676, #13182663, #13182669, …
maximal quotient ofC11×#3946, C11×#3947, C11×#3952, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 75);