Finite Group Databasebeta

#44526127

order30944
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

FittingC2×C8×C967 ⋊ C2
SylowC967 ⋊ #131

Subgroups

subgroupG/H
centerC8C2×D967
commutator, socleC2×C967C22×C4
FrattiniC4C22×D967
FittingC2×C8×C967C2
prime radical#29509171C2
cosocleC4×C967C23
hypercenterC2×C8D967
hypocenterC967#131
LCSG ▷ C2×C967 ▷ C967
UCSC1 ◁ C8 ◁ C2×C8

62 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15472

Polycyclic presentation:

2^5,967|a^2=d,d^2=e,c^b=ce,f^c=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, 152);