Finite Group Databasebeta

← Prev (#11724913) Next (#11724915) →

C11×#683 #11724914

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

Aliases

direct productC11×#683

Splittings

HallC5×C11 ⋊ C4⋊C4
SylowC5 ⋊ C11×C4⋊C4

Subgroups

subgroupG/H
centerC22×C11C2×D5
commutatorC2×C5C2×C4×C11
FrattiniC22C2×D5×C11
FittingC2×C4×C5×C11C2
socle, prime radicalC22×C5×C11C22
cosocleC22×C5C22×C11
hypercenterC2×C4×C11D5
hypocenterC5C11×C4⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C11 ◁ C2×C4×C11

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 880

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)(17,18,19,20)(22,24);(13,14)(15,16)(21,22,23,24)

Conjugacy classes & character table

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

Relationships

maximal subgroup of#13182701, #13182707, #13182710, …
maximal normal subgroup of#13182701, #13182707, #13182710, …
maximal quotient ofC11×#3939, C11×#3940, C11×#3946, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 82);