Finite Group Databasebeta

← Prev (#44394351) Next (#44394353) →

Dic5×C23×C7⋊C9 #44394352

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

Aliases

direct productDic5×C23×C7⋊C9
unambiguous semidirect product(C7×Dic5)⋊(C9×C23)
unambiguous semidirect product(C7×Dic5×C23)⋊C9

Splittings

derived, HallC5×C7 ⋊ C4×C9×C23
HallC5×C23×C7⋊C9 ⋊ C4
HallC7×Dic5×C23 ⋊ C9
HallC5×C7×C23 ⋊ C4×C9
HallC5×C7⋊C9 ⋊ C4×C23
HallC7×C23 ⋊ C9×Dic5
HallC7×Dic5 ⋊ C9×C23
HallC5×C23 ⋊ C4×C7⋊C9
SylowC7 ⋊ C9×Dic5×C23
SylowC5 ⋊ C4×C23×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C4×C9×C23
FrattiniC2×C3D5×ΓL(1,𝔽8)×C23
Fitting, socle, prime radicalC2×C3×C5×C7×C23C2×C3
cosocleC2×C3×C5×C7C2×C3×C23
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C23

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28980

Conjugacy classes & character table

2760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 21);