Finite Group Databasebeta

← Prev (#38737288) Next (#38737290) →

C3×C7×Dic299 #38737289

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

Aliases

direct productC3×C7×Dic299
unambiguous semidirect productC23⋊(C3×C7×Dic13)

Splittings

derived, HallC13×C23 ⋊ C3×C4×C7
HallC3×C7×C13×C23 ⋊ C4
HallC7×C13×C23 ⋊ C3×C4
HallC3×C13×C23 ⋊ C4×C7
HallC3×C7×C23 ⋊ Dic13
HallC3×C7×C13 ⋊ Dic23
HallC7×C23 ⋊ C3×Dic13
HallC7×C13 ⋊ C3×Dic23
HallC3×C23 ⋊ C7×Dic13
HallC3×C13 ⋊ C7×Dic23
SylowC23 ⋊ C3×C7×Dic13
SylowC13 ⋊ C3×C7×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D299
commutator, hypocenterC13×C23C3×C4×C7
FrattiniC2C3×C7×D299
Fitting, socle, prime radicalC2×C3×C7×C13×C23C2
cosocleC2×C13×C23C2×C3×C7
LCSG ▷ C13×C23
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25116

Conjugacy classes & character table

6342 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 8);