Finite Group Databasebeta

#28399163

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

SylowC113 ⋊ #2911

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
FittingC2×#117×C113C2
socleC22×C113C22×D4
prime radicalC24×C113D4
cosocleC2×C4×C113C24
hypercenterC2×#117D113
hypocenterC113#2911
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3616

Polycyclic presentation:

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

Conjugacy classes & character table

2284 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 13099);