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D33×D91 #26046565

order12012
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD33×D91

Splittings

Fitting, socle, derived, HallC3×C7×C11×C13 ⋊ C22
HallC7×C11×C13 ⋊ C2×D3
HallC3×C11×C13 ⋊ C2×D7
HallC3×C7×C13 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ D3×D7
HallC7×C13 ⋊ C2×D33
HallC7×C11 ⋊ D3×D13
HallC3×C13 ⋊ D7×D11
HallC3×C11 ⋊ C2×D91
HallC3×C7 ⋊ D11×D13
SylowC13 ⋊ D7×D33
SylowC11 ⋊ D3×D91
SylowC7 ⋊ D13×D33
SylowC3 ⋊ D11×D91

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C13C22
LCSG ▷ C3×C7×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

846 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD91×D99, D33×#10587722, D33×#10587723, …
maximal normal subgroup ofD33×#10587722, D33×#10587723, D33×ΓL(1,𝔽8)⋊D13, …
maximal quotient ofD91×D99, C3×D33×D91, D33×D273, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 155);