Finite Group Databasebeta

#44526040

order30944
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC967 ⋊ #101

Subgroups

subgroupG/H
centerC2C22⋊Dic967
commutator, prime radicalC22×C967C2×C4
FrattiniC2×C4C2×D967
FittingC2×Q8×C967C2
socleC2×C967C22⋊C4
cosocleC2×C4×C967C22
hypercenterC2×Q8D967
hypocenterC967#101
LCSG ▷ C22×C967 ▷ C2×C967 ▷ C967
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q8

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15472

Polycyclic presentation:

2^5,967|a^2=d,b^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^966,d^b=de

Conjugacy classes & character table

4841 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30944, 65);