Finite Group Databasebeta

#44530598

order31264
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC977 ⋊ #106

Subgroups

subgroupG/H
centerC22D3908
commutatorC4×C977C2×C4
FrattiniC2×C4C2×D977
FittingC2×C8×C977C2
socle, prime radicalC22×C977D4
cosocleC2×C4×C977C22
hypercenterC2×C8D977
hypocenterC977#106
LCSG ▷ C4×C977 ▷ C2×C977 ▷ C977
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31264

Polycyclic presentation:

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

Conjugacy classes & character table

7822 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31264, 78);