Finite Group Databasebeta

C23×#14268637 #28405296

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

Aliases

direct productC23×#14268637

Splittings

SylowC113 ⋊ C23×Q16

Subgroups

subgroupG/H
centerC24C22⋊D113
commutator, cosocleC4×C113C25
FrattiniC4C24×D113
FittingC23×Q8×C113C2
socle, prime radicalC24×C113D4
hypercenterC23×Q8D113
hypocenterC113C23×Q16
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×Q8

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14464

Conjugacy classes & character table

2296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 19232);