Finite Group Databasebeta

C2×C22⋊Dic971 #44527103

order31072
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊Dic971

Splittings

SylowC971 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D971
commutatorC2×C971C22×C4
FrattiniC22C22×D971
Fitting, prime radicalC24×C971C2
socleC23×C971C22
cosocleC22×C971C23
hypercenterC24D971
hypocenterC971C2×C22⋊C4
LCSG ▷ C2×C971 ▷ C971
UCSC1 ◁ C23 ◁ C24

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15536

Conjugacy classes & character table

7780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31072, 98);