Finite Group Databasebeta

#380×D277 #47985536

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

Aliases

direct product#380×D277

Splittings

Fitting#380×C277 ⋊ C2
SylowC277 ⋊ C2×#380

Subgroups

subgroupG/H
center, FrattiniC23C23×D277
commutatorC22×C277C23×C4
Fitting#380×C277C2
socle, cosocleC23×C277C24
prime radicalC24×D277C22
hypercenter#380D277
hypocenterC277C2×#380
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C23 ◁ #380

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8864

Conjugacy classes & character table

3920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35456, 6879);