Finite Group Databasebeta

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C2×C11×D11×C7⋊C9 #44478944

order30492
automorphism?
homologyAbelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D11×C7⋊C9
unambiguous semidirect productC11⋊(C22×C11×C7⋊C9)
unambiguous semidirect product(C2×C11)⋊(C2×C11×C7⋊C9)
unambiguous semidirect product(C2×C7×D11)⋊(C9×C11)
unambiguous semidirect product(C2×C7×C11×D11)⋊C9

Splittings

derivedC7×C11 ⋊ C22×C9×C11
HallC112×C7⋊C9 ⋊ C22
HallC2×C7×C11×D11 ⋊ C9
HallC7×C112 ⋊ C22×C9
SylowC112 ⋊ C22×C7⋊C9
SylowC7 ⋊ C2×C9×C11×D11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C22×C9×C11
FrattiniC3C2×C11×ΓL(1,𝔽8)×D11
Fitting, socleC2×C3×C7×C112C2×C3
prime radicalC2×C3×C7×C11×D11C3
cosocleC3×C7×C11C22×C3×C11
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C11

180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 2772

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 167);