Finite Group Databasebeta

← Prev (#44526221) Next (#44526223) →

C2×C7×C11×C67⋊C3 #44526222

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

Aliases

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

Splittings

Fitting, socle, HallC2×C7×C11×C67 ⋊ C3
derived, SylowC67 ⋊ C2×C3×C7×C11
HallC7×C11×C67 ⋊ C2×C3
HallC2×C11×C67 ⋊ C3×C7
HallC2×C7×C67 ⋊ C3×C11
HallC11×C67 ⋊ C2×C3×C7
HallC7×C67 ⋊ C2×C3×C11
HallC2×C67 ⋊ C3×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11C67⋊C3
commutator, cosocle, hypocenterC67C2×C3×C7×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C67C3
LCSG ▷ C67
UCSC1 ◁ C2×C7×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10318

Conjugacy classes & character table

3850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 3);