Finite Group Databasebeta

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C2×C3×C7×C67⋊C11 #44526221

order30954
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C7×C67⋊C11
unambiguous semidirect product(C2×C3×C67)⋊(C7×C11)
unambiguous semidirect product(C2×C3×C7×C67)⋊C11

Splittings

Fitting, socle, HallC2×C3×C7×C67 ⋊ C11
derived, SylowC67 ⋊ C2×C3×C7×C11
HallC3×C7×C67 ⋊ C2×C11
HallC2×C7×C67 ⋊ C3×C11
HallC7×C67 ⋊ C2×C3×C11
HallC2×C3×C67 ⋊ C7×C11
HallC3×C67 ⋊ C2×C7×C11
HallC2×C67 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C67⋊C11
commutator, cosocle, hypocenterC67C2×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C3×C7×C67C11
LCSG ▷ C67
UCSC1 ◁ C2×C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2814

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 2);