Finite Group Databasebeta

C2×C4⋊Dic977 #44530621

order31264
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊Dic977

Splittings

SylowC977 ⋊ C2×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×D977
commutatorC2×C977C22×C4
FrattiniC22C22×D977
FittingC22×C4×C977C2
socle, prime radicalC23×C977C22
cosocleC22×C977C23
hypercenterC22×C4D977
hypocenterC977C2×C4⋊C4
LCSG ▷ C2×C977 ▷ C977
UCSC1 ◁ C23 ◁ C22×C4

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31264

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, 101);