Finite Group Databasebeta

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#47985563

order35456
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

No aliases for this group.

Splittings

FittingC4×C4⋊C4×C277 ⋊ C2
SylowC277 ⋊ #2283

Subgroups

subgroupG/H
centerC22×C4C22×D277
commutatorC22×C277C23×C4
FrattiniC23C23×D277
FittingC4×C4⋊C4×C277C2
socle, cosocleC23×C277C24
prime radicalC23×D277C23
hypercenterC4×C4⋊C4D277
hypocenterC277#2283
LCSG ▷ C22×C277 ▷ C277
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17728

Polycyclic presentation:

2^7,277|a^2=g,b^2=f,d^2=e,b^a=be,c^a=cf,h^b=h^276,h^c=h^276

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, 6906);