Finite Group Databasebeta

← Prev (#38737285) Next (#38737287) →

C4×C23×#63271 #38737286

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

Aliases

direct productC4×C23×#63271

Splittings

Fitting, HallC4×C7×C13×C23 ⋊ C3
derived, HallC7×C13 ⋊ C3×C4×C23
HallC7×C13×C23 ⋊ C3×C4
HallC4×C13×C23 ⋊ ΓL(1,𝔽8)
HallC4×C7×C23 ⋊ C13⋊C3
HallC4×C7×C13 ⋊ C3×C23
HallC13×C23 ⋊ C4×ΓL(1,𝔽8)
HallC7×C23 ⋊ C4×C13⋊C3
HallC4×C13 ⋊ ΓL(1,𝔽8)×C23
HallC4×C7 ⋊ C23×C13⋊C3
SylowC13 ⋊ C4×ΓL(1,𝔽8)×C23
SylowC7 ⋊ C4×C23×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C23#63271
commutator, hypocenterC7×C13C3×C4×C23
FrattiniC2C2×C23×#63271
FittingC4×C7×C13×C23C3
socleC2×C7×C13×C23C2×C3
prime radicalC2×C23×#63271C2
cosocleC2×C7×C13C2×C3×C23
LCSG ▷ C7×C13
UCSC1 ◁ C4×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8372

Conjugacy classes & character table

3036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 5);