Finite Group Databasebeta

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D21×C67⋊C11 #44526250

order30954
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productD21×C67⋊C11
unambiguous semidirect productC3⋊(D7×C67⋊C11)
unambiguous semidirect productC7⋊(D3×C67⋊C11)
unambiguous semidirect product(D21×C67)⋊C11

Splittings

Fitting, socle, derived, HallC3×C7×C67 ⋊ C2×C11
HallC3×C7×C67⋊C11 ⋊ C2
HallC7×C67⋊C11 ⋊ D3
HallD21×C67 ⋊ C11
HallC3×C67⋊C11 ⋊ D7
HallC7×C67 ⋊ D3×C11
HallC3×C67 ⋊ C11×D7
SylowC67 ⋊ C11×D21
HallC3×C7 ⋊ C2×C67⋊C11
SylowC7 ⋊ D3×C67⋊C11
SylowC3 ⋊ D7×C67⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C67C2×C11
LCSG ▷ C3×C7×C67
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1407

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 31);