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D33×ΓL(1,𝔽32) #23779461

order10230
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productD33×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(D11×ΓL(1,𝔽32))

Splittings

Fitting, socle, derived, HallC3×C11×C31 ⋊ C2×C5
HallC3×C11×ΓL(1,𝔽32) ⋊ C2
HallC31×D33 ⋊ C5
HallC11×ΓL(1,𝔽32) ⋊ D3
HallC3×ΓL(1,𝔽32) ⋊ D11
HallC11×C31 ⋊ C5×D3
HallC3×C31 ⋊ C5×D11
HallC3×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×D33
SylowC11 ⋊ D3×ΓL(1,𝔽32)
SylowC3 ⋊ D11×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C31C2×C5
LCSG ▷ C3×C11×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD33×D31⋊C5, (C3⋊(D31⋊C5))⋊D11, D3×D11×ΓL(1,𝔽32), …
maximal normal subgroup ofD33×D31⋊C5, (C3⋊(D31⋊C5))⋊D11, D3×D11×ΓL(1,𝔽32), …
maximal quotient ofDic33×ΓL(1,𝔽32), C2×D33×ΓL(1,𝔽32), ΓL(1,𝔽32)×D99, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 60);