Finite Group Databasebeta

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C3×D3×C7×C11⋊D11 #44479190

order30492
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2×C11

Aliases

direct productC3×D3×C7×C11⋊D11
unambiguous semidirect product(D3×C11)⋊(C3×C7×D11)

Splittings

Fitting, socle, HallC32×C7×C112 ⋊ C22
derivedC3×C112 ⋊ C22×C3×C7
HallC32×C112 ⋊ C22×C7
HallC7×C112 ⋊ C2×C3×D3
SylowC112 ⋊ C2×C3×D3×C7
HallC32×C7 ⋊ C2×C11⋊D11
SylowC32 ⋊ C2×C7×C11⋊D11

Subgroups

subgroupG/H
center, hypercenterC3×C7D3×C11⋊D11
commutator, cosocle, hypocenterC3×C112C22×C3×C7
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C3×C112
UCSC1 ◁ C3×C7

616 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degreeμ(G) = 35
transitive degreeμt(G) = 5082

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3)(4,5,6)(7,8,9,10,11,12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(26,27)(28,29)(30,31)(32,33)(34,35);(5,6)(25,26,28,30,32,34,35,33,31,29,27);(14,15,17,19,21,23,24,22,20,18,16)

Conjugacy classes & character table

3906 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 413);