Finite Group Databasebeta

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C2×C7⋊C9×C11⋊D11 #44478945

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×C11⋊D11
commutator, hypocenterC7×C112C22×C9
FrattiniC3C2×ΓL(1,𝔽8)×C11⋊D11
Fitting, socleC2×C3×C7×C112C2×C3
prime radicalC2×C3×C7×C11⋊D11C3
cosocleC3×C7×C112C22×C3
LCSG ▷ C7×C112
UCSC1 ◁ C2×C3

420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15246

Conjugacy classes & character table

1860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 168);