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C2×(C11⋊D11)⋊(C7⋊C9) #44478946

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

Aliases

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

Splittings

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

Subgroups

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

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1386

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 169);