Finite Group Databasebeta

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C2×C32×C5×C7×D23 #44394662

order28980
automorphism?
homologyAbelianization (H1) = C22×C32×C5×C7 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C5×C7×D23
unambiguous semidirect productC23⋊(C22×C32×C5×C7)
unambiguous semidirect product(C2×C23)⋊(C2×C32×C5×C7)

Splittings

Fitting, socleC2×C32×C5×C7×C23 ⋊ C2
derived, SylowC23 ⋊ C22×C32×C5×C7
HallC32×C5×C7×C23 ⋊ C22
HallC32×C7×C23 ⋊ C22×C5
HallC32×C5×C23 ⋊ C22×C7
HallC5×C7×C23 ⋊ C22×C32
HallC32×C23 ⋊ C22×C5×C7
HallC7×C23 ⋊ C22×C32×C5
HallC5×C23 ⋊ C22×C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5×C7D23
commutator, cosocle, hypocenterC23C22×C32×C5×C7
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C23C2
LCSG ▷ C23
UCSC1 ◁ C2×C32×C5×C7

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14490

Conjugacy classes & character table

8190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 331);