Finite Group Databasebeta

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C2×C3×C11×D231 #44479266

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

Aliases

direct productC2×C3×C11×D231
unambiguous semidirect product(C2×C3)⋊(C3×C11×D77)
unambiguous semidirect product(C2×C11)⋊(C3×C11×D21)

Splittings

Fitting, socleC2×C32×C7×C112 ⋊ C2
derivedC3×C7×C11 ⋊ C22×C3×C11
HallC32×C7×C112 ⋊ C22
HallC32×C112 ⋊ C2×D7
HallC7×C112 ⋊ C2×C3×D3
SylowC112 ⋊ C2×C3×D21
HallC32×C7 ⋊ C2×C11×D11
SylowC32 ⋊ C2×C11×D77
SylowC7 ⋊ C2×C3×C11×D33

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D231
commutator, cosocle, hypocenterC3×C7×C11C22×C3×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C112C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C3×C11

296 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 924

Conjugacy classes & character table

7722 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 489);