Finite Group Databasebeta

#44530581

order31264
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

SylowC977 ⋊ #99

Subgroups

subgroupG/H
centerC2C22⋊Dic977
commutatorC22×C977C2×C4
FrattiniC23C2×D977
Fitting, prime radicalC2×D4×C977C2
socleC2×C977C22⋊C4
cosocleC23×C977C22
hypercenterC2×D4D977
hypocenterC977#99
LCSG ▷ C22×C977 ▷ C2×C977 ▷ C977
UCSC1 ◁ C2 ◁ C23 ◁ C2×D4

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7816

Polycyclic presentation:

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

Conjugacy classes & character table

4891 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31264, 61);