Finite Group Databasebeta

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C11×C3⋊((C79⋊C3)⋊C4) #44530874

order31284
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊((C79⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C11×(C79⋊C3)⋊C4)
unambiguous semidirect product(C79⋊C3)⋊(C11×Dic3)
unambiguous semidirect productDic237⋊(C3×C11)
unambiguous semidirect product(C11×Dic237)⋊C3

Splittings

derivedC3×C79 ⋊ C3×C4×C11
HallC3×C11×C79⋊C3 ⋊ C4
HallC11×C79 ⋊ C3×Dic3
HallC3×C79⋊C3 ⋊ C4×C11
SylowC79 ⋊ C3×C11×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊(D79⋊C3)
commutator, hypocenterC3×C79C3×C4×C11
FrattiniC2C11×C3⋊(D79⋊C3)
Fitting, socleC2×C3×C11×C79C2×C3
prime radicalC2×C3×C11×C79⋊C3C2
cosocleC2×C3×C79C2×C3×C11
LCSG ▷ C3×C79
UCSC1 ◁ C2×C11

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10428

Conjugacy classes & character table

1056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31284, 39);