Finite Group Databasebeta

#44470520

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

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #520

Subgroups

subgroupG/H
center, FrattiniC22C23×D467
commutatorC2×C467C23×C4
Fitting, prime radicalC2×#41×C467C2
socle, cosocleC22×C467C24
hypercenterC2×#41D467
hypocenterC467#520
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C22 ◁ C2×#41

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Polycyclic presentation:

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

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, 1032);