Finite Group Databasebeta

C2×C22⋊Dic977 #44530618

order31264
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊Dic977

Splittings

SylowC977 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D977
commutatorC2×C977C22×C4
FrattiniC22C22×D977
Fitting, prime radicalC24×C977C2
socleC23×C977C22
cosocleC22×C977C23
hypercenterC24D977
hypocenterC977C2×C22⋊C4
LCSG ▷ C2×C977 ▷ C977
UCSC1 ◁ C23 ◁ C24

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15632

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, 98);