Finite Group Databasebeta

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C11×(C67⋊C3)⋊D7 #44526268

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

Aliases

direct productC11×(C67⋊C3)⋊D7

Splittings

Fitting, socle, HallC7×C11×C67 ⋊ C2×C3
derived, HallC7×C67 ⋊ C2×C3×C11
HallC7×C11×C67⋊C3 ⋊ C2
HallC11×D469 ⋊ C3
HallC11×C67⋊C3 ⋊ D7
HallC7×C67⋊C3 ⋊ C2×C11
HallD469 ⋊ C3×C11
HallC11×C67 ⋊ C3×D7
HallC67⋊C3 ⋊ C11×D7
HallC7×C11 ⋊ D67⋊C3
SylowC67 ⋊ C3×C11×D7
SylowC7 ⋊ C11×D67⋊C3

Subgroups

subgroupG/H
center, hypercenterC11(C67⋊C3)⋊D7
commutator, cosocle, hypocenterC7×C67C2×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C67C2×C3
LCSG ▷ C7×C67
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5159

Conjugacy classes & character table

1012 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 49);