Finite Group Databasebeta

#44470446

order29888
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #501

Subgroups

subgroupG/H
centerC22C2×D1868
commutator, cosocleC2×C4×C467C23
FrattiniC2×C4C22×D467
Fitting#97×C467C2
socle, prime radicalC22×C467C2×D4
hypercenter#97D467
hypocenterC467#501
LCSG ▷ C2×C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C22 ◁ C42 ◁ #97

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29888

Polycyclic presentation:

2^6,467|a^2=d,b^2=d,c^2=e,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^466,c^b=cf

Conjugacy classes & character table

4676 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 958);