Finite Group Databasebeta

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C7×C11×(C31⋊C3)⋊C4 #43270602

order28644
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×(C31⋊C3)⋊C4
unambiguous semidirect product(C31⋊C3)⋊(C4×C7×C11)
unambiguous semidirect productDic31⋊(C3×C7×C11)
unambiguous semidirect product(C11×Dic31)⋊(C3×C7)

Splittings

derived, SylowC31 ⋊ C3×C4×C7×C11
HallC7×C11×Dic31 ⋊ C3
HallC7×C11×C31⋊C3 ⋊ C4
HallC7×C11×C31 ⋊ C3×C4
HallC11×Dic31 ⋊ C3×C7
HallC11×C31⋊C3 ⋊ C4×C7
HallC7×Dic31 ⋊ C3×C11
HallC7×C31⋊C3 ⋊ C4×C11
HallC11×C31 ⋊ C3×C4×C7
HallC7×C31 ⋊ C3×C4×C11
HallDic31 ⋊ C3×C7×C11
HallC31⋊C3 ⋊ C4×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11D31⋊C3
commutator, hypocenterC31C3×C4×C7×C11
FrattiniC2C7×C11×D31⋊C3
Fitting, socleC2×C7×C11×C31C2×C3
prime radicalC2×C7×C11×C31⋊C3C2
cosocleC2×C31C2×C3×C7×C11
LCSG ▷ C31
UCSC1 ◁ C2×C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9548

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28644, 21);