Finite Group Databasebeta

#44470514

order29888
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #519

Subgroups

subgroupG/H
center, FrattiniC22C23×D467
commutatorC2×C467C23×C4
Fitting#117×C467C2
socle, cosocleC22×C467C24
prime radicalC23×C467C23
hypercenter#117D467
hypocenterC467#519
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C22 ◁ #117

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Polycyclic presentation:

2^6,467|a^2=f,b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,g^c=g^466

Conjugacy classes & character table

4694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 1026);