Finite Group Databasebeta

← Prev (#38737403) Next (#38737405) →

C3×C7×C23⋊#261 #38737404

order25116
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C23⋊#261
unambiguous semidirect productC23⋊(C3×C7×#261)

Splittings

Fitting, socle, HallC3×C7×C13×C23 ⋊ C4
derived, HallC13×C23 ⋊ C3×C4×C7
HallC7×C13×C23 ⋊ C3×C4
HallC3×C13×C23 ⋊ C4×C7
HallC3×C7×C23 ⋊ #261
HallC3×C7×C13 ⋊ Dic23
HallC7×C23 ⋊ C3×#261
HallC7×C13 ⋊ C3×Dic23
HallC3×C23 ⋊ C7×#261
HallC3×C13 ⋊ C7×Dic23
SylowC23 ⋊ C3×C7×#261
SylowC13 ⋊ C3×C7×Dic23

Subgroups

subgroupG/H
center, hypercenterC3×C7C23⋊#261
commutator, hypocenterC13×C23C3×C4×C7
FrattiniC1G
Fitting, socleC3×C7×C13×C23C4
prime radicalC3×C7×C23×D13C2
cosocleC23×D13C2×C3×C7
LCSG ▷ C13×C23
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6279

Conjugacy classes & character table

1995 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 123);