Finite Group Databasebeta

← Prev (#38737406) Next (#38737408) →

C3×C23×C7⋊#261 #38737407

order25116
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×C7⋊#261

Splittings

Fitting, socle, HallC3×C7×C13×C23 ⋊ C4
derived, HallC7×C13 ⋊ C3×C4×C23
HallC7×C13×C23 ⋊ C3×C4
HallC3×C13×C23 ⋊ Dic7
HallC3×C7×C23 ⋊ #261
HallC13×C23 ⋊ C3×Dic7
HallC3×C7×C13 ⋊ C4×C23
HallC7×C23 ⋊ C3×#261
HallC3×C13 ⋊ C23×Dic7
HallC3×C7 ⋊ C23×#261
SylowC13 ⋊ C3×C23×Dic7
SylowC7 ⋊ C3×C23×#261

Subgroups

subgroupG/H
center, hypercenterC3×C23C7⋊#261
commutator, hypocenterC7×C13C3×C4×C23
FrattiniC1G
Fitting, socleC3×C7×C13×C23C4
prime radicalC3×C7×C23×D13C2
cosocleC7×D13C2×C3×C23
LCSG ▷ C7×C13
UCSC1 ◁ C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6279

Conjugacy classes & character table

2139 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 126);