Finite Group Databasebeta

#44470087

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

Aliases

No aliases for this group.

Splittings

SylowC467 ⋊ #431

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D467
commutatorC2×C467C22×C8
FittingC22⋊C8×C467C2
socleC22×C467C22×C4
prime radicalC23×C467C2×C4
cosocleC2×C4×C467C23
hypercenterC22⋊C8D467
hypocenterC467#431
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C2×C4 ◁ C22⋊C8

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^c=g^466

Conjugacy classes & character table

4700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 599);