Finite Group Databasebeta

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C7×C11×C3⋊C8 #14270425

order1848
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C7×C8×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×C3⋊C8
unambiguous semidirect productC3⋊(C7×C8×C11)

Splittings

derived, SylowC3 ⋊ C7×C8×C11
HallC3×C7×C11 ⋊ C8
HallC3×C11 ⋊ C7×C8
HallC3×C7 ⋊ C8×C11

Subgroups

subgroupG/H
center, hypercenterC4×C7×C11D3
commutator, hypocenterC3C7×C8×C11
FrattiniC4D3×C7×C11
FittingC3×C4×C7×C11C2
socle, prime radicalC2×C3×C7×C11C4
cosocleC3×C4C2×C7×C11
LCSG ▷ C3
UCSC1 ◁ C4×C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 1848

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18)(20,21)(22,23,24,26,25,27,28,29);(19,20,21)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1848, 8);