Finite Group Databasebeta

#44530606

order31264
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC977 ⋊ M32

Subgroups

subgroupG/H
center, FrattiniC8C2×D977
commutator, socleC2×C977C2×C8
FittingC2×C8×C977C2
prime radicalC22×C977C8
cosocleC8×C977C22
hypercenterC2×C8D977
hypocenterC977M32
LCSG ▷ C2×C977 ▷ C977
UCSC1 ◁ C8 ◁ C2×C8

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15632

Polycyclic presentation:

2^5,977|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^976

Conjugacy classes & character table

7828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31264, 86);