Finite Group Databasebeta

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C23×Dic315 #44394347

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

Aliases

direct productC23×Dic315
unambiguous semidirect productC7⋊(C23×Dic45)
unambiguous semidirect productC9⋊(C23×Dic35)

Splittings

derived, HallC5×C7×C9 ⋊ C4×C23
HallC5×C7×C9×C23 ⋊ C4
HallC7×C9×C23 ⋊ Dic5
HallC5×C9×C23 ⋊ Dic7
HallC5×C7×C23 ⋊ Dic9
HallC9×C23 ⋊ Dic35
HallC7×C23 ⋊ Dic45
HallC5×C23 ⋊ Dic63
HallC7×C9 ⋊ Dic5×C23
HallC5×C9 ⋊ C23×Dic7
HallC5×C7 ⋊ C23×Dic9
SylowC9 ⋊ C23×Dic35
SylowC7 ⋊ C23×Dic45
SylowC5 ⋊ C23×Dic63

Subgroups

subgroupG/H
center, hypercenterC2×C23D315
commutator, hypocenterC5×C7×C9C4×C23
FrattiniC2×C3C23×D105
FittingC2×C5×C7×C9×C23C2
socle, prime radicalC2×C3×C5×C7×C23D3
cosocleC2×C5×C7×C9C2×C23
LCSG ▷ C5×C7×C9
UCSC1 ◁ C2×C23

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28980

Conjugacy classes & character table

7314 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28980, 16);