Finite Group Databasebeta

C7⋊C9×C373 #37555049

order23499
automorphism?
homologyAbelianization (H1) = C9×C373 · Schur multiplier (H2) = C1

Aliases

direct productC7⋊C9×C373
unambiguous semidirect productC7⋊(C9×C373)

Splittings

derived, SylowC7 ⋊ C9×C373
HallC7×C373 ⋊ C9

Subgroups

subgroupG/H
center, hypercenterC3×C373ΓL(1,𝔽8)
commutator, hypocenterC7C9×C373
FrattiniC3ΓL(1,𝔽8)×C373
Fitting, socle, prime radicalC3×C7×C373C3
cosocleC3×C7C3×C373
LCSG ▷ C7
UCSC1 ◁ C3×C373

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23499

Conjugacy classes & character table

5595 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23499, 2);