Finite Group Databasebeta

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C43×Dic31⋊C5 #40998617

order26660
automorphism?
homologyAbelianization (H1) = C4×C5×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×Dic31⋊C5
unambiguous semidirect productDic31⋊(C5×C43)
unambiguous semidirect productΓL(1,𝔽32)⋊(C4×C43)
unambiguous semidirect product(C43×Dic31)⋊C5

Splittings

derived, SylowC31 ⋊ C4×C5×C43
HallC43×ΓL(1,𝔽32) ⋊ C4
HallC43×Dic31 ⋊ C5
HallC31×C43 ⋊ C4×C5
HallΓL(1,𝔽32) ⋊ C4×C43
HallDic31 ⋊ C5×C43

Subgroups

subgroupG/H
center, hypercenterC2×C43D31⋊C5
commutator, hypocenterC31C4×C5×C43
FrattiniC2C43×D31⋊C5
Fitting, socleC2×C31×C43C2×C5
prime radicalC2×C43×ΓL(1,𝔽32)C2
cosocleC2×C31C2×C5×C43
LCSG ▷ C31
UCSC1 ◁ C2×C43

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5332

Conjugacy classes & character table

1118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26660, 11);