Finite Group Databasebeta

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C2×C5×C23×C3⋊D21 #44394679

order28980
automorphism?
homologyAbelianization (H1) = C22×C5×C23 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C23×C3⋊D21
unambiguous semidirect product(C2×C3)⋊(C5×C23×D21)
unambiguous semidirect product(C2×C7)⋊(C5×C3⋊D3×C23)

Splittings

Fitting, socleC2×C32×C5×C7×C23 ⋊ C2
derived, HallC32×C7 ⋊ C22×C5×C23
HallC32×C5×C7×C23 ⋊ C22
HallC32×C7×C23 ⋊ C22×C5
HallC32×C5×C23 ⋊ C2×D7
HallC5×C7×C23 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C22×C23
HallC32×C23 ⋊ C2×C5×D7
HallC7×C23 ⋊ C2×C5×C3⋊D3
HallC32×C5 ⋊ C2×D7×C23
HallC5×C7 ⋊ C2×C3⋊D3×C23
SylowC32 ⋊ C2×C5×D7×C23
SylowC7 ⋊ C2×C5×C3⋊D3×C23

Subgroups

subgroupG/H
center, hypercenterC2×C5×C23C3⋊D21
commutator, cosocle, hypocenterC32×C7C22×C5×C23
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C23C2
LCSG ▷ C32×C7
UCSC1 ◁ C2×C5×C23

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14490

Conjugacy classes & character table

7590 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 348);