Finite Group Databasebeta

C23×Dic452 #28405297

order14464
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC23×Dic452

Splittings

SylowC113 ⋊ C23×Q16

Subgroups

subgroupG/H
centerC24D452
commutator, cosocleC4×C113C25
FrattiniC4C24×D113
FittingC23×C8×C113C2
socle, prime radicalC24×C113D4
hypercenterC23×C8D113
hypocenterC113C23×Q16
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14464

Conjugacy classes & character table

3640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 19233);