Finite Group Databasebeta

C23×#14268657 #28407561

order14464
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC23×#14268657

Splittings

SylowC113 ⋊ C23×M16

Subgroups

subgroupG/H
centerC24C2×#90673
commutatorC2×C113C24×C4
FrattiniC2C24×#90673
FittingC23×C4×C113C4
socleC24×C113C2×C4
prime radicalC24×D113C4
cosocleDic113C25
hypercenterC23×C4#90673
hypocenterC113C23×M16
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C24 ◁ C23×C4

1720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21497);