Finite Group Databasebeta

← Prev (#38764181) Next (#38764183) →

C2×C3×ΓL(1,𝔽8)×D101 #38764182

order25452
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×ΓL(1,𝔽8)×D101
unambiguous semidirect productC101⋊(C22×C3×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C101)⋊(C2×C3×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×D101)⋊C32
unambiguous semidirect product(C2×C3×C7×D101)⋊C3

Splittings

Fitting, socleC2×C3×C7×C101 ⋊ C2×C3
derived, HallC7×C101 ⋊ C22×C32
HallC3×ΓL(1,𝔽8)×C101 ⋊ C22
HallC2×C7×D101 ⋊ C32
SylowC101 ⋊ C22×C3×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C32×D101

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×D101
commutator, cosocle, hypocenterC7×C101C22×C32
FrattiniC1G
Fitting, socleC2×C3×C7×C101C2×C3
LCSG ▷ C7×C101
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4242

Conjugacy classes & character table

1560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25452, 76);