Finite Group Databasebeta

#44470090

order29888
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #431

Subgroups

subgroupG/H
centerC42C2×D467
commutatorC2×C467C22×C8
FrattiniC2×C4C22×D467
FittingC2×C42×C467C2
socleC22×C467C22×C4
prime radicalC23×C467C2×C4
cosocleC2×C4×C467C23
hypercenterC2×C42D467
hypocenterC467#431
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C42 ◁ C2×C42

118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14944

Polycyclic presentation:

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

Conjugacy classes & character table

7496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 602);