Finite Group Databasebeta

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C11×#807 #11760587

order1056
isoclinismisoclinic class of #213
automorphism?
homologyAbelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×#807

Splittings

HallC3×C11 ⋊ #107
SylowC3 ⋊ C11×#107

Subgroups

subgroupG/H
centerC22×C11#67
commutatorC3×C4C2×C4×C11
FrattiniC2×C4C2×D3×C11
FittingC3×C11×C4⋊C4C2
socle, prime radicalC22×C3×C11D4
cosocleC2×C3×C4C22×C11
hypercenterC11×C4⋊C4D3
hypocenterC3C11×#107
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C11 ◁ C2×C4×C11 ◁ C11×C4⋊C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 1056

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14)(15,16,17,18)(20,23)(21,26)(24,25);(13,14)(19,20,21,24,22,25,26,23)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1056, 124);