Finite Group Databasebeta

C22⋊C4×D773 #37612940

order24736
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D773

Splittings

FittingC22⋊C4×C773 ⋊ C2
SylowC773 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D773
commutatorC2×C773C22×C4
FittingC22⋊C4×C773C2
socle, cosocleC22×C773C23
prime radicalC23×D773C2
hypercenterC22⋊C4D773
hypocenterC773C2×C22⋊C4
LCSG ▷ C2×C773 ▷ C773
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6184

Conjugacy classes & character table

3880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24736, 96);