Finite Group Databasebeta

← Prev (#38737292) Next (#38737294) →

C3×Dic2093 #38737293

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

Aliases

direct productC3×Dic2093
unambiguous semidirect productC23⋊(C3×Dic91)

Splittings

derived, HallC7×C13×C23 ⋊ C3×C4
HallC3×C7×C13×C23 ⋊ C4
HallC3×C13×C23 ⋊ Dic7
HallC3×C7×C23 ⋊ Dic13
HallC13×C23 ⋊ C3×Dic7
HallC3×C7×C13 ⋊ Dic23
HallC7×C23 ⋊ C3×Dic13
HallC7×C13 ⋊ C3×Dic23
HallC3×C23 ⋊ Dic91
HallC3×C13 ⋊ Dic161
SylowC23 ⋊ C3×Dic91
HallC3×C7 ⋊ Dic299
SylowC13 ⋊ C3×Dic161
SylowC7 ⋊ C3×Dic299

Subgroups

subgroupG/H
center, hypercenterC2×C3D2093
commutator, hypocenterC7×C13×C23C3×C4
FrattiniC2C3×D2093
Fitting, socle, prime radicalC2×C3×C7×C13×C23C2
cosocleC2×C7×C13×C23C2×C3
LCSG ▷ C7×C13×C23
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25116

Conjugacy classes & character table

6288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 12);