Finite Group Databasebeta

#43249481

order28432
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1777 ⋊ SD16

Subgroups

subgroupG/H
centerC2C22⋊D1777
commutator, cosocleC4×C1777C22
FrattiniC4C2×D1777
Fitting, prime radicalD4×C1777C2
socleC2×C1777D4
hypercenterD4D1777
hypocenterC1777SD16
LCSG ▷ C4×C1777 ▷ C2×C1777 ▷ C1777
UCSC1 ◁ C2 ◁ C4 ◁ D4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14216

Polycyclic presentation:

2^4,1777|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1776,c^b=cd

Conjugacy classes & character table

4447 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28432, 28);