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#45666798

order32896
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4

Aliases

No aliases for this group.

Splittings

SylowC257 ⋊ #2295

Subgroups

subgroupG/H
centerC22×C4C22×D257
commutatorC22×C257C23×C4
FrattiniC23C23×D257
FittingC2×C4×Q8×C257C2
socle, prime radical, cosocleC23×C257C24
hypercenterC2×C4×Q8D257
hypocenterC257#2295
LCSG ▷ C22×C257 ▷ C257
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32896

Polycyclic presentation:

2^7,257|a^2=g,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^256,h^b=h^256

Conjugacy classes & character table

5176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32896, 6988);