Finite Group Databasebeta

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C4×C5×C23×C7⋊C9 #44394333

order28980
automorphism?
homologyAbelianization (H1) = C4×C5×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C23×C7⋊C9
unambiguous semidirect product(C4×C7)⋊(C5×C9×C23)
unambiguous semidirect product(C4×C5×C7)⋊(C9×C23)
unambiguous semidirect product(C4×C7×C23)⋊(C5×C9)
unambiguous semidirect product(C4×C5×C7×C23)⋊C9

Splittings

derived, SylowC7 ⋊ C4×C5×C9×C23
HallC4×C5×C7×C23 ⋊ C9
HallC5×C7×C23 ⋊ C4×C9
HallC4×C7×C23 ⋊ C5×C9
HallC7×C23 ⋊ C4×C5×C9
HallC4×C5×C7 ⋊ C9×C23
HallC5×C7 ⋊ C4×C9×C23
HallC4×C7 ⋊ C5×C9×C23

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5×C23ΓL(1,𝔽8)
commutator, hypocenterC7C4×C5×C9×C23
FrattiniC2×C3C2×C5×ΓL(1,𝔽8)×C23
FittingC3×C4×C5×C7×C23C3
socle, prime radicalC2×C3×C5×C7×C23C2×C3
cosocleC2×C3×C7C2×C3×C5×C23
LCSG ▷ C7
UCSC1 ◁ C3×C4×C5×C23

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28980

Conjugacy classes & character table

6900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 2);