Finite Group Databasebeta

← Prev (#38737295) Next (#38737297) →

C7×C23×Dic39 #38737296

order25116
automorphism?
homologyAbelianization (H1) = C4×C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC7×C23×Dic39
unambiguous semidirect productC3⋊(C7×C23×Dic13)

Splittings

derived, HallC3×C13 ⋊ C4×C7×C23
HallC3×C7×C13×C23 ⋊ C4
HallC7×C13×C23 ⋊ Dic3
HallC3×C13×C23 ⋊ C4×C7
HallC3×C7×C23 ⋊ Dic13
HallC13×C23 ⋊ C7×Dic3
HallC3×C7×C13 ⋊ C4×C23
HallC7×C13 ⋊ Dic3×C23
HallC3×C23 ⋊ C7×Dic13
HallC3×C7 ⋊ C23×Dic13
SylowC13 ⋊ C7×Dic3×C23
SylowC3 ⋊ C7×C23×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C7×C23D39
commutator, hypocenterC3×C13C4×C7×C23
FrattiniC2C7×C23×D39
Fitting, socle, prime radicalC2×C3×C7×C13×C23C2
cosocleC2×C3×C13C2×C7×C23
LCSG ▷ C3×C13
UCSC1 ◁ C2×C7×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25116

Conjugacy classes & character table

6762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 15);