Finite Group Databasebeta

#44525366

order30896
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1931 ⋊ M16

Subgroups

subgroupG/H
center, FrattiniC4C2×D1931
commutator, socleC2×C1931C2×C4
FittingC2×C4×C1931C2
prime radicalC22×C1931C4
cosocleC4×C1931C22
hypercenterC2×C4D1931
hypocenterC1931M16
LCSG ▷ C2×C1931 ▷ C1931
UCSC1 ◁ C4 ◁ C2×C4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15448

Polycyclic presentation:

2^4,1931|a^2=c,c^2=d,b^a=bd,e^a=e^1930

Conjugacy classes & character table

7730 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30896, 24);