Finite Group Databasebeta

← Prev (#47985670) Next (#47985672) →

C4×#22579850 #47985671

order35456
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC4×#22579850

Splittings

FittingC4×C22⋊C4×C277 ⋊ C2
SylowC277 ⋊ C4×#120

Subgroups

subgroupG/H
centerC22×C4C22×D277
commutatorC22×C277C23×C4
FrattiniC23C23×D277
FittingC4×C22⋊C4×C277C2
socle, cosocleC23×C277C24
prime radicalC2×#22579850C2
hypercenterC4×C22⋊C4D277
hypocenterC277C4×#120
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

1224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8864

Conjugacy classes & character table

5576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35456, 7014);