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C3×C112×C22⋊ΓL(1,𝔽8) #44479253

order30492
automorphism?
homologyAbelianization (H1) = C32×C112 · Schur multiplier (H2) = C2×C3×C11

Aliases

direct productC3×C112×C22⋊ΓL(1,𝔽8)
unambiguous semidirect product(C22×C3)⋊(C112×ΓL(1,𝔽8))
unambiguous semidirect product(C3×C7)⋊(C112×A4)
unambiguous semidirect product(C22×C3×C11)⋊(C11×ΓL(1,𝔽8))
unambiguous semidirect product(C3×C7×C11)⋊(C11×A4)

Splittings

Fitting, socleC22×C3×C7×C112 ⋊ C3
derived, HallC22×C7 ⋊ C32×C112
HallC22×C7×C112 ⋊ C32
HallC7×C112 ⋊ C3×A4
HallC22×C112 ⋊ C3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C112×A4
SylowC22 ⋊ C3×C112×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC3×C112C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C32×C112
FrattiniC1G
Fitting, socleC22×C3×C7×C112C3
LCSG ▷ C22×C7
UCSC1 ◁ C3×C112

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10164

Conjugacy classes & character table

4356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 476);