Finite Group Databasebeta

C2×C22⋊Dic773 #37612942

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

Aliases

direct productC2×C22⋊Dic773

Splittings

SylowC773 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
centerC23C2×D773
commutatorC2×C773C22×C4
FrattiniC22C22×D773
Fitting, prime radicalC24×C773C2
socleC23×C773C22
cosocleC22×C773C23
hypercenterC24D773
hypocenterC773C2×C22⋊C4
LCSG ▷ C2×C773 ▷ C773
UCSC1 ◁ C23 ◁ C24

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12368

Conjugacy classes & character table

6196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24736, 98);