Finite Group Databasebeta

#44525767

order30928
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1933 ⋊ M16

Subgroups

subgroupG/H
center, FrattiniC4C2×D1933
commutator, socleC2×C1933C2×C4
FittingC2×C4×C1933C2
prime radicalC22×C1933C4
cosocleC4×C1933C22
hypercenterC2×C4D1933
hypocenterC1933M16
LCSG ▷ C2×C1933 ▷ C1933
UCSC1 ◁ C4 ◁ C2×C4

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15464

Polycyclic presentation:

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

Conjugacy classes & character table

7738 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30928, 24);