Finite Group Databasebeta

#44526031

order30944
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC967 ⋊ #97

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D967
commutatorC2×C967C42
FittingC2×C8×C967C2
socle, prime radicalC22×C967C2×C4
cosocleC2×C4×C967C22
hypercenterC2×C8D967
hypocenterC967#97
LCSG ▷ C2×C967 ▷ C967
UCSC1 ◁ C2×C4 ◁ C2×C8

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30944

Polycyclic presentation:

2^5,967|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^966

Conjugacy classes & character table

7748 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30944, 56);