Finite Group Databasebeta

C23×C22⋊Dic23 #15686555

order2944
isoclinismisoclinic class of Dic46
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×C22⋊Dic23

Splittings

SylowC23 ⋊ C23×C22⋊C4

Subgroups

subgroupG/H
centerC25C2×D23
commutatorC2×C23C24×C4
FrattiniC22C24×D23
Fitting, prime radicalC26×C23C2
socleC25×C23C22
cosocleC22×C23C25
hypercenterC26D23
hypocenterC23C23×C22⋊C4
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C25 ◁ C26

4632 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 17668);