Finite Group Databasebeta

#44525773

order30928
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1933 ⋊ Q16

Subgroups

subgroupG/H
centerC2C22⋊D1933
commutator, cosocleC4×C1933C22
FrattiniC4C2×D1933
FittingQ8×C1933C2
socle, prime radicalC2×C1933D4
hypercenterQ8D1933
hypocenterC1933Q16
LCSG ▷ C4×C1933 ▷ C2×C1933 ▷ C1933
UCSC1 ◁ C2 ◁ C4 ◁ Q8

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30928

Polycyclic presentation:

2^4,1933|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^1932

Conjugacy classes & character table

4837 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30928, 30);