Finite Group Databasebeta

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C3×C5×(C127⋊C3)⋊C4 #37504010

order22860
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×(C127⋊C3)⋊C4
unambiguous semidirect product(C127⋊C3)⋊(C3×C4×C5)
unambiguous semidirect productDic127⋊(C32×C5)
unambiguous semidirect product(C3×Dic127)⋊(C3×C5)
unambiguous semidirect product(C5×Dic127)⋊C32
unambiguous semidirect product(C3×C5×Dic127)⋊C3

Splittings

derived, SylowC127 ⋊ C32×C4×C5
HallC3×C5×C127⋊C3 ⋊ C4
HallC5×Dic127 ⋊ C32
HallC3×C127⋊C3 ⋊ C4×C5
HallC5×C127 ⋊ C32×C4
HallDic127 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D127⋊C3
commutator, hypocenterC127C32×C4×C5
FrattiniC2C3×C5×D127⋊C3
Fitting, socleC2×C3×C5×C127C2×C3
prime radicalC2×C3×C5×C127⋊C3C2
cosocleC2×C127C2×C32×C5
LCSG ▷ C127
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7620

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22860, 46);