Finite Group Databasebeta

← Prev (#37528309) Next (#37528311) →

C22×C11×ΓL(1,𝔽8)×C25 #37528310

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC22×C11×ΓL(1,𝔽8)×C25

Splittings

Fitting, HallC22×C7×C11×C25 ⋊ C3
derived, SylowC7 ⋊ C22×C3×C11×C25
HallC7×C11×C25 ⋊ C22×C3
HallC22×C7×C25 ⋊ C3×C11
HallC22×C7×C11 ⋊ C3×C25
HallC7×C25 ⋊ C22×C3×C11
HallC7×C11 ⋊ C22×C3×C25
HallC22×C7 ⋊ C3×C11×C25

Subgroups

subgroupG/H
center, hypercenterC22×C11×C25ΓL(1,𝔽8)
commutator, hypocenterC7C22×C3×C11×C25
FrattiniC5C22×C5×C11×ΓL(1,𝔽8)
FittingC22×C7×C11×C25C3
socleC22×C5×C7×C11C3×C5
prime radicalC22×C5×C11×ΓL(1,𝔽8)C5
cosocleC5×C7C22×C3×C5×C11
LCSG ▷ C7
UCSC1 ◁ C22×C11×C25

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

5500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 121);