Finite Group Databasebeta

C17×C23×C7⋊C9 #37590147

order24633
automorphism?
homologyAbelianization (H1) = C9×C17×C23 · Schur multiplier (H2) = C1

Aliases

direct productC17×C23×C7⋊C9
unambiguous semidirect productC7⋊(C9×C17×C23)
unambiguous semidirect product(C7×C17)⋊(C9×C23)
unambiguous semidirect product(C7×C23)⋊(C9×C17)
unambiguous semidirect product(C7×C17×C23)⋊C9

Splittings

derived, SylowC7 ⋊ C9×C17×C23
HallC7×C17×C23 ⋊ C9
HallC7×C23 ⋊ C9×C17
HallC7×C17 ⋊ C9×C23

Subgroups

subgroupG/H
center, hypercenterC3×C17×C23ΓL(1,𝔽8)
commutator, hypocenterC7C9×C17×C23
FrattiniC3C17×ΓL(1,𝔽8)×C23
Fitting, socle, prime radicalC3×C7×C17×C23C3
cosocleC3×C7C3×C17×C23
LCSG ▷ C7
UCSC1 ◁ C3×C17×C23

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24633

Conjugacy classes & character table

5865 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24633, 2);