Finite Group Databasebeta

C22⋊C4×D971 #44527101

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

Aliases

direct productC22⋊C4×D971

Splittings

FittingC22⋊C4×C971 ⋊ C2
SylowC971 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D971
commutatorC2×C971C22×C4
FittingC22⋊C4×C971C2
socle, cosocleC22×C971C23
prime radicalC23×D971C2
hypercenterC22⋊C4D971
hypocenterC971C2×C22⋊C4
LCSG ▷ C2×C971 ▷ C971
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7768

Conjugacy classes & character table

4870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31072, 96);