Finite Group Databasebeta

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C11×#4247 #14270477

order1848
isoclinismisoclinic class of #4245
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×#4247

Splittings

HallC3×C7×C11 ⋊ D4
HallC7×C11 ⋊ D12
HallC3×C11 ⋊ C22⋊D7
HallC3×C7 ⋊ D4×C11
SylowC7 ⋊ C11×D12
SylowC3 ⋊ C11×C22⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C11D3×D7
commutator, cosocleC2×C3×C7C22×C11
FrattiniC2D3×C11×D7
Fitting, socleC2×C3×C7×C11C22
hypocenterC3×C7D4×C11
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 924

A minimal faithful permutation representation — 2 generators on 25 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1848, 60);