Finite Group Databasebeta

C23×Dic23⋊C4 #15686557

order2944
isoclinismisoclinic class of Dic46
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC23×Dic23⋊C4

Splittings

SylowC23 ⋊ C23×C4⋊C4

Subgroups

subgroupG/H
centerC25C2×D23
commutatorC2×C23C24×C4
FrattiniC22C24×D23
FittingC24×C4×C23C2
socle, prime radicalC25×C23C22
cosocleC22×C23C25
hypercenterC24×C4D23
hypocenterC23C23×C4⋊C4
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C25 ◁ C24×C4

2488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2944

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, 17670);