Finite Group Databasebeta

#28399207

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4

Aliases

No aliases for this group.

Splittings

SylowC113 ⋊ #2920

Subgroups

subgroupG/H
centerC42C22×D113
commutator, socleC22×C113C23×C4
FrattiniC2×C4C23×D113
FittingC22×C42×C113C2
prime radicalC24×C113C2×C4
cosocleC2×C4×C113C24
hypercenterC22×C42D113
hypocenterC113#2920
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C42 ◁ C22×C42

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Polycyclic presentation:

2^7,113|a^2=f,c^2=e,f^2=g,b^a=be,d^a=dg,h^a=h^112

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, 13143);